Updated on 2025/06/06

写真a

 
KATORI Makoto
 
Organization
Faculty of Science and Engineering Professor
Other responsible organization
Physics Course of Graduate School of Science and Engineering, Master's Program
Physics Course of Graduate School of Science and Engineering, Doctoral Program
Homepage
https://sites.google.com/g.chuo-u.ac.jp/katori-english/home?authuser=0
External link

Degree

  • Doctor of Science ( The University of Tokyo )

  • 理学修士 ( 東京大学 )

Education

  • 1988.3
     

    The University of Tokyo   Graduate School, Division of Science   Physics   doctor course   completed

  • 1984.3
     

    The University of Tokyo   Faculty of Science   Department of Physics   graduated

Research History

  • 1999.4 - 　

    ～ 中央大学理工学部教授

  • 1999.4 - 　

    Chuo University, Faculty of Science and Engineering, Professor

  • 1993.4 - 1999.3

    Chuo University   Faculty of Science and Engineering

  • 1993.4 - 1999.3

    . Chuo University, Faculty of Science and Engineering, Associate Professor

  • 1992.4 - 1993.3

    Chuo University   Faculty of Science and Engineering

  • 1992.4 - 1993.3

    . Chuo University, Faculty of Science and Engineering, Lecturer

  • 1988.4 - 1992.3

    The University of Tokyo   Faculty of Science

  • 1988.4 - 1992.3

    . The University of Tokyo, Faculty of Science, Research Associate

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Professional Memberships

  • THE JAPANESE SOCIETY FOR MATHEMATICAL BIOLOGY

  • 日本物理学会

  • 日本数学会

  • The Physical Society of Japan

  • The Mathematical Society of Japan

Research Interests

  • Stochastic Analysis

  • Random Matrix Theory

  • 確率論

  • Phase Transitions and Critical Phenomena

  • 統計力学

  • 数理物理学

  • Probability Theory

  • Statistical Physics

  • Mathematical Physics

Research Areas

  • Natural Science / Mathematical physics and fundamental theory of condensed matter physics

  • Natural Science / Basic analysis

Papers

  • Three-Parametric Marcenko--Pastur Density Reviewed International journal

    Taiki Endo, Makoto Katori

    Journal of Statistical Physics   178 ( 6 )   1397 - 1416   2020.2

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    Authorship：Last author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer  

    The complex Wishart ensemble is the statistical ensemble
    of $M \times N$ complex random matrices with $M \geq N$
    such that the real and imaginary parts of each element
    are given by independent standard normal variables.
    The Marcenko--Pastur (MP) density $\rho(x; r), x \geq 0$
    describes the distribution for squares of the
    singular values of the random matrices in this ensemble
    in the scaling limit $N \to \infty$, $M \to \infty$ with
    a fixed rectangularity $r=N/M \in (0, 1]$.
    The dynamical extension of the squared-singular-value distribution
    is realized by the noncolliding squared Bessel process,
    and its hydrodynamic limit provides the
    two-parametric MP density $\rho(x; r, t)$ with time $t \geq 0$,
    whose initial distribution is $\delta(x)$.
    Recently, Blaizot, Nowak, and Warcho{\l}
    studied the time-dependent complex Wishart ensemble
    with an external source and introduced
    the three-parametric MP density
    $\rho(x; r, t, a)$ by analyzing the
    hydrodynamic limit of the process starting from $\delta(x-a), a > 0$.
    In the present paper, we give useful expressions
    for $\rho(x; r, t, a)$ and perform a systematic study
    of dynamic critical phenomena
    observed at the critical time $t_{\rm c}(a)=a$ when $r=1$.
    The universal behavior in the long-term limit
    $t \to \infty$ is also reported.
    It is expected that the present system having
    the three-parametric MP density provides
    a mean-field model for QCD
    showing spontaneous chiral symmetry breaking.

    DOI： 10.1007/s10955-020-02511-5

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  • Switching particle systems for foraging ants showing phase transitions in path selections Reviewed

    Ayana Ezoe, Saori Morimoto, Yuya Tanaka, Makoto Katori, Hiraku Nishimori

    Physica A: Statistical Mechanics and its Applications   643   129798 - 129798   2024.6

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    Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    Switching interacting particle systems studied in probability theory are the stochastic processes of hopping particles on a lattice made up of slow and fast particles, where the switching between these types of particles occurs randomly at a given transition rate. This paper explores how such stochastic processes involving multiple particles can model group behaviors of ants. Recent experimental research by the last author’s group has investigated how ants switch between two types of primarily relied cues to select foraging paths based on the current situation. Here, we propose a discrete-time interacting random walk model on a square lattice, incorporating two types of hopping rules. Numerical simulation results demonstrate global changes in selected homing paths, transitioning from trailing paths of the ‘pheromone road’ to nearly optimal paths depending on the switching parameters. By introducing two types of order parameters characterizing the dependence of homing duration distributions on switching parameters, we discuss these global changes as phase transitions in ant path selections. We also study critical phenomena associated with continuous phase transitions.

    DOI： 10.1016/j.physa.2024.129798

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  • From random surfaces to random point processes and random curves: GFF, Dyson model, and multiple SLE Invited

    Makoto Katori

    61 ( 3 )   44 - 50   2023.3

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    Authorship：Lead author   Language：Japanese   Publishing type：Part of collection (book)  

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  • Local universality of determinantal point processes on Riemannian manifolds Reviewed International journal

    Makoto Katori, Tomoyuki Shirai

    Proc. Japan Acad. Ser. A Math. Sci.   98 ( 10 )   95 - 100   2022.12

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：The Japan Academy  

    We consider the Laplace-Beltrami operator $\Delta_g$ on
    a smooth, compact Riemannian manifold $(M,g)$
    and the determinantal point process $\xila$ on $M$ associated with the spectral
    projection of $-\Delta_g$ onto the subspace corresponding to the eigenvalues up to
    $\la^2$.
    We show that the pull-back of $\xila$ by the exponential map
    $\exp_p : T_p^*M \to M$ under a suitable scaling converges
    weakly to the universal determinantal point process on
    $T_p^* M$ as $\la \to \infty$.

    DOI： 10.3792/pjaa.98.018

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  • Hyperuniformity of the determinantal point processes associated with the Heisenberg group Invited International journal

    Makoto Katori

    RIMS Kokyuroku   2235 ( 1 )   12 - 29   2022.12

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    Authorship：Lead author   Language：English   Publishing type：Research paper (bulletin of university, research institution)   Publisher：Research Institute for Mathematical Sciences, Kyoto University  

    The Ginibre point process is given by the eigenvalue
    distribution of a non-hermitian complex Gaussian matrix
    in the infinite matrix-size limit.
    This is a determinantal point process (DPP) on the complex
    plane $\C$ in the sense that all correlation functions
    are given by determinants specified by an integral
    kernel called the correlation kernel.
    Shirai introduced the one-parameter
    ($m \in \N_0$) extensions of the Ginibre DPP
    and called them
    the Ginibre-type point processes.
    In the present paper we consider a generalization
    of the Ginibre and the Ginibre-type point processes on $\C$
    to the DPPs in the higher-dimensional spaces,
    $\C^D, D=2,3, \dots$, in which
    they are parameterized by a multivariate level
    $m \in \N_0^D$.
    We call the obtained point processes
    the extended Heisenberg family of DPPs,
    since the correlation kernels are generally
    identified with the correlations of two points in
    the space of Heisenberg group expressed by
    the Schr\"{o}dinger representations.
    We prove that all DPPs in this large family are
    in Class I of hyperuniformity.

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  • Functional Equations Solving Initial-Value Problems of Complex Burgers-Type Equations for One-Dimensional Log-Gases Reviewed International journal

    Taiki Endo, Makoto Katori, Noriyoshi Sakuma

    Symmetry, Integrability and Geometry: Methods and Applications   049   1 - 22   2022.7

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    Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：SIGMA (Symmetry, Integrability and Geometry: Methods and Application)  

    We study the hydrodynamic limits of three kinds of one-dimensional stochastic log-gases known as Dyson's Brownian motion model, its chiral version, and the Bru-Wishart process studied in dynamical random matrix theory. We define the measure-valued processes so that their Cauchy transforms solve the complex Burgers-type equations. We show that applications of the method of characteristic curves to these partial differential equations provide the functional equations relating the Cauchy transforms of measures at an arbitrary time with those at the initial time. We transform the functional equations for the Cauchy transforms to those for the R-transforms and the S-transforms of the measures, which play central roles in free probability theory. The obtained functional equations for the R-transforms and the S-transforms are simpler than those for the Cauchy transforms and useful for explicit calculations including the computation of free cumulant sequences. Some of the results are argued using the notion of free convolutions.

    DOI： 10.3842/sigma.2022.049

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    Other Link： https://www.emis.de/journals/SIGMA/non-commutative-probability.html

  • Partial isometries, duality, and determinantal point processes Reviewed

    Makoto Katori, Tomoyuki Shirai

    Random Matrices: Theory and Applications   11 ( 03 )   2250025/1 - 2250025/70   2022.7

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    Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：World Scientific Pub Co Pte Ltd  

    A determinantal point process (DPP) is an ensemble of random nonnegative-integer-valued Radon measures [Formula: see text] on a space S with measure [Formula: see text], whose correlation functions are all given by determinants specified by an integral kernel K called the correlation kernel. We consider a pair of Hilbert spaces, [Formula: see text], which are assumed to be realized as [Formula: see text]-spaces, [Formula: see text], [Formula: see text], and introduce a bounded linear operator [Formula: see text] and its adjoint [Formula: see text]. We show that if [Formula: see text] is a partial isometry of locally Hilbert–Schmidt class, then we have a unique DPP [Formula: see text] associated with [Formula: see text]. In addition, if [Formula: see text] is also of locally Hilbert–Schmidt class, then we have a unique pair of DPPs, [Formula: see text], [Formula: see text]. We also give a practical framework which makes [Formula: see text] and [Formula: see text] satisfy the above conditions. Our framework to construct pairs of DPPs implies useful duality relations between DPPs making pairs. For a correlation kernel of a given DPP our formula can provide plural different expressions, which reveal different aspects of the DPP. In order to demonstrate these advantages of our framework as well as to show that the class of DPPs obtained by this method is large enough to study universal structures in a variety of DPPs, we report plenty of examples of DPPs in one-, two- and higher-dimensional spaces S, where several types of weak convergence from finite DPPs to infinite DPPs are given. One-parameter ([Formula: see text]) series of infinite DPPs on [Formula: see text] and [Formula: see text] are discussed, which we call the Euclidean and the Heisenberg families of DPPs, respectively, following the terminologies of Zelditch.

    DOI： 10.1142/s2010326322500253

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  • Zeros of the i.i.d. Gaussian Laurent Series on an Annulus: Weighted Szeg ˝o Kernels and Permanental-Determinantal Point Processes Reviewed International journal

    Makoto Katori, Tomoyuki Shirai

    Communications in Mathematical Physics   392 ( 3 )   1099 - 1151   2022.5

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    Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer  

    DOI： 10.1007/s00220-022-04365-2

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  • Gaussian free fields coupled with multiple SLEs driven by stochastic log-gases Invited Reviewed International journal

    Makoto Katori, Shinji Koshida

    Advanced Studies in Pure Mathematics   87   315 - 340   2021.11

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    Authorship：Lead author   Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Mathematical Society of Japan  

    Miller and Sheffield introduced the notion of
    an imaginary surface as an equivalence class
    of pairs of simply connected proper subdomains of
    $\C$ and Gaussian free fields (GFFs)
    on them under the conformal equivalence.
    They considered the situation in which
    the conformal transformations are given by
    a chordal Schramm--Loewner evolution (SLE).
    In the present paper, we construct
    GFF-valued processes on $\H$ (the upper half-plane)
    and $\O$ (the first orthant of $\C$)
    by coupling a GFF with a multiple SLE evolving in time on each domain.
    We prove that a GFF on $\H$ and $\O$ is (locally) coupled
    with a multiple SLE if the multiple SLE is driven
    by a stochastic log-gas called the Dyson model defined
    on $\R$ and the Bru--Wishart process
    defined on $\R_+$, respectively.
    We obtain pairs of time-evolutionary domains
    with multiple-slits and GFF-valued processes.

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  • Three phases of multiple SLE driven by non-colliding Dyson's Brownian motions Reviewed International journal

    Makoto Katori, Shinji Koshida

    Journal of Physics A: Mathematical and Theoretical   54 ( 32 )   325002/1 - 325002/19   2021.6

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP Publishing  

    The present paper is concerned with properties of multiple Schramm–
    Loewner evolutions (SLEs) labelled by a parameter κ ∈ (0, 8]. Specifically, we consider
    the solution of the multiple Loewner equation driven by a time change of Dyson’s
    Brownian motions in the non-colliding regime. Although it is often considered that
    several properties of the solution can be studied by means of commutation relations
    of SLEs and the absolute continuity, this method is available only in the case that the
    curves generated by commuting SLEs are separated. Beyond this restriction, it is not
    even obvious that the solution of the multiple Loewner equation generates multiple
    curves. To overcome this difficulty, we employ the coupling of Gaussian free fields and
    multiple SLEs. Consequently, we prove the longstanding conjecture that the solution
    indeed generates multiple continuous curves. Furthermore, these multiple curves are
    (i) simple disjoint curves when κ ∈ (0, 4], (ii) intersecting curves when κ ∈ (4, 8), and
    (iii) space-filling curves when κ = 8.

    DOI： 10.1088/1751-8121/ac0dee

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  • Continuum percolation and stochastic epidemic models on Poisson and Ginibre point processes Reviewed International journal

    Machiko Katori, Makoto Katori

    Physica A: Statistical Mechanics and its Applications   581   126191/1 - 126191/14   2021.6

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    The most studied continuum percolation model in two dimensions is the Boolean model consisting of disks with the same radius whose centers are randomly distributed on the Poisson point process (PPP). We also consider the Boolean percolation model on the Ginibre point process (GPP) which is a typical repelling point process realizing hyperuniformity. We think that the PPP approximates a disordered configuration of individuals, while the GPP does a configuration of citizens adopting a strategy to keep social distancing in a city in order to avoid contagion. We consider the SIR models with contagious infection on supercritical percolation clusters formed on the PPP and the GPP. By numerical simulations, we studied dependence of the percolation phenomena and the infection processes on the PPP- and the GPP-underlying graphs. We show that in a subcritical regime of infection rate the PPP-based models show emergence of infection clusters on clumping of points which is formed by fluctuation of uncorrelated Poissonian statistics. On the other hand, the cumulative numbers of infected individuals in processes are suppressed in the GPP-based models.

    DOI： 10.1016/j.physa.2021.126191

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  • Local number variances and hyperuniformity of the Heisenberg family of determinantal point processes Reviewed International journal

    Takato Matsui, Makoto Katori, Tomoyuki Shirai

    Journal of Physics A: Mathematical and Theoretical   54 ( 16 )   165201/1 - 165201/22   2021.4

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    Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP Publishing  

    The bulk scaling limit of eigenvalue distribution
    on the complex plane ${\mathbb{C } }$
    of the complex Ginibre random matrices provides
    a determinantal point process (DPP).
    This point process is a typical example of
    disordered hyperuniform system characterized
    by an anomalous suppression of large-scale
    density fluctuations.
    As extensions of the Ginibre DPP, we consider
    a family of DPPs defined on the $D$-dimensional
    complex spaces ${\mathbb{C } }$, $D \in {\mathbb{N } }$, in which
    the Ginibre DPP is realized when $D=1$.
    This one-parameter family ($D \in {\mathbb{N } }$) of DPPs
    is called the Heisenberg family,
    since the correlation kernels are
    identified with the Szeg\H{o} kernels for the
    reduced Heisenberg group.
    For each $D$, using the modified Bessel functions,
    an exact and useful expression
    is shown for the local number variance
    of points included in a ball with radius $R$
    in ${\mathbb{R } }^{2D} \simeq {\mathbb{C } }^D$.
    We prove that any DPP in the Heisenberg family is in the
    hyperuniform state of Class I,
    in the sense that the number variance
    behaves as $R^{2D-1}$ as $R \to \infty$.
    Our exact results provide asymptotic expansions
    of the number variances in large $R$.

    DOI： 10.1088/1751-8121/abecaa

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    Other Link： https://iopscience.iop.org/article/10.1088/1751-8121/abecaa/pdf

  • Conformal welding problem, flow line problem, and multiple Schramm–Loewner evolution Reviewed

    Makoto Katori, Shinji Koshida

    Journal of Mathematical Physics   61 ( 8 )   083301 - 083301   2020.8

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：AIP Publishing  

    DOI： 10.1063/1.5145357

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  • Scaling limit for determinantal point processes on spheres Invited Reviewed International journal

    Makoto Katori, Tomoyuki Shirai

    RIMS Kokyuroku Bessatsu   B79   123 - 138   2020.4

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    Authorship：Lead author   Language：English   Publishing type：Research paper (bulletin of university, research institution)   Publisher：Research Institute for Mathematical Sciences, Kyoto University  

    The unitary group with the Haar probability measure
    is called Circular Unitary Ensemble.
    All the eigenvalues lie on the unit
    circle in the complex plane and they can be regarded as a
    determinantal point process on ${\mathbb{S } }^1$.
    It is also known that
    the scaled point processes converge weakly to the determinantal point
    process associated with the so-called sine kernel
    as the size of matrices tends to $\infty$.
    We extend this result to the case of high-dimensional spheres
    and show that the scaling limit processes are determinantal
    point processes associated with the kernels expressed by the
    Bessel functions of the first kind.

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  • Two-Dimensional Elliptic Determinantal Point Processes and Related Systems Reviewed

    KATORI Makoto

    Communications in Mathematical Physics   371 ( 3 )   1283 - 1321   2019.11

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    We introduce new families of determinantal point processes (DPPs)<br />
    on a complex plane ${\mathbb{C } }$, which are classified into seven types<br />
    following the irreducible reduced affine root systems,<br />
    $R_N=A_{N-1}$, $B_N$, $B^{\vee}_N$, $C_N$, $C^{\vee}_N$, $BC_N$, $D_N$,<br />
    $N \in {\mathbb{N } }$. <br />
    Their multivariate probability densities are doubly periodic<br />
    with periods $(L, iW)$, $0 &lt; L, W &lt; \infty$, $i=\sqrt{-1}$.<br />
    The construction is based on the orthogonality relations <br />
    with respect to the double integrals over the fundamental domain,<br />
    $[0, L) \times i [0, W)$, which are proved in this paper <br />
    for the $R_N$-theta functions introduced by Rosengren and Schlosser.<br />
    In the scaling limit $N \to \infty, L \to \infty$<br />
    with constant density<br />
    $\rho=N/(LW)$ and constant $W$, we obtain four types of<br />
    DPPs with an infinite number of<br />
    points on ${\mathbb{C } }$, which have periodicity with period $i W$. <br />
    In the further limit $W \to \infty$ with constant $\rho$,<br />
    they are degenerated into three infinite-dimensional DPPs.<br />
    One of them is uniform on ${\mathbb{C } }$ and equivalent <br />
    with the Ginibre point process<br />
    studied in random matrix theory, while<br />
    other two systems are rotationally symmetric around the origin,<br />
    but non-uniform on ${\mathbb{C } }$.<br />
    We show that the elliptic DPP<br />
    of type $A_{N-1}$ is identified with the particle section,<br />
    obtained by subtracting the background effect, <br />
    of the two-dimensional exactly solvable model<br />
    for one-component plasma studied by Forrester.<br />
    Other two exactly solvable models of one-component plasma <br />
    are constructed associated with the elliptic DPPs <br />
    of types $C_N$ and $D_N$.<br />
    Relationship to the Gaussian free field on a torus<br />
    is discussed for these three exactly solvable plasma models.

    DOI： 10.1007/s00220-019-03351-5

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  • Macdonald denominators for affine root systems, orthogonal theta functions, and elliptic determinantal point processes Reviewed

    KATORI Makoto

    Journal of Mathematical Physics   60 ( 1 )   013301/1 - 013301/27   2019.4

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    Rosengren and Schlosser introduced notions of<br />
    $\RN$-theta functions for the seven types of<br />
    irreducible reduced affine root systems,<br />
    $\RN=\AN$, $\BN$, $\BNv$, $\CN$, $\CNv$, $\BCN$, $\DN$, $N \in \N$,<br />
    and gave the Macdonald denominator formulas.<br />
    We prove that, if the variables of the<br />
    $\RN$-theta functions are properly scaled<br />
    with $N$, they construct seven sets of biorthogonal <br />
    functions, each of which has a continuous parameter<br />
    $t \in (0, t_{\ast})$ with given $0&lt; t_{\ast} &lt; \infty$.<br />
    Following the standard method in random matrix theory,<br />
    we introduce seven types of one-parameter<br />
    ($t \in (0, t_{\ast})$) families of determinantal point processes<br />
    in one dimension,<br />
    in which the correlation kernels are expressed by<br />
    the biorthogonal theta functions.<br />
    We demonstrate that they are elliptic extensions of<br />
    the classical determinantal point processes<br />
    whose correlation kernels are expressed by<br />
    trigonometric and rational functions.<br />
    In the scaling limits associated with $N \to \infty$,<br />
    we obtain four types of elliptic determinantal point<br />
    processes with an infinite number of points<br />
    and parameter $t \in (0, t_{\ast})$.<br />
    We give new expressions for<br />
    the Macdonald denominators using <br />
    the Karlin--McGregor--Lindstr\&quot;om--Gessel--Viennot<br />
    determinants for noncolliding Brownian paths,<br />
    and show the realization of the associated <br />
    elliptic determinantal point processes<br />
    as noncolliding Brownian brides <br />
    with a time duration $t_{\ast}$, which are<br />
    specified by the pinned configurations<br />
    at time $t=0$ and $t=t_{\ast}$.

    DOI： 10.1063/1.5037805

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  • Excursion Processes Associated with Elliptic Combinatorics Reviewed

    Hiroya Baba, Makoto Katori

    Journal of Statistical Physics   171 ( 6 )   1035 - 1066   2018.6

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer New York LLC  

    DOI： 10.1007/s10955-018-2045-6

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  • Hydrodynamic Limit of Multiple SLE Reviewed

    Ikkei Hotta, Makoto Katori

    Journal of Statistical Physics   171 ( 1 )   166 - 188   2018.3

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    Recently del Monaco and Schlei{\ss}inger addressed <br />
    an interesting problem whether one can take the limit of<br />
    multiple Schramm--Loewner evolution (SLE) <br />
    as the number of slits $N$ goes to infinity.<br />
    When the $N$ slits grow from points on the real line $\R$<br />
    in a simultaneous way and go to infinity<br />
    within the upper half plane $\H$,<br />
    an ordinary differential equation <br />
    describing time evolution of the conformal map $g_t(z)$<br />
    was derived in the $N \to \infty$ limit, <br />
    which is coupled with a complex Burgers equation<br />
    in the inviscid limit. <br />
    It is well known that the complex Burgers equation<br />
    governs the hydrodynamic limit of the Dyson model<br />
    defined on $\R$ studied in random matrix theory, <br />
    and when all particles start from<br />
    the origin, the solution of this Burgers equation is given<br />
    by the Stieltjes transformation of the measure which<br />
    follows a time-dependent version of Wigner&#039;s semicircle law.<br />
    In the present paper, first we study the hydrodynamic limit<br />
    of the multiple SLE in the case that all <br />
    slits start from the origin. <br />
    We show that the time-dependent version of Wigner&#039;s <br />
    semicircle law determines the time evolution<br />
    of the SLE hull, $K_t \subset \H\cup \R$ ,<br />
    in this hydrodynamic limit. <br />
    Next we consider the situation such that <br />
    a half number of the slits start from $a&gt;0$ and<br />
    another half of slits start from $-a &lt; 0$,<br />
    and determine the multiple SLE in the <br />
    hydrodynamic limit. <br />
    After reporting these exact solutions,<br />
    we will discuss the universal long-term behavior of <br />
    the multiple SLE and its hull $K_t$ in the hydrodynamic limit.

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  • Percolation of optical excitation mediated by near-field interactions Reviewed

    Makoto Naruse, Song-Ju Kim, Taiki Takahashi, Masashi Aono, Kouichi Akahane, Mario D'Acunto, Hirokazu Hori, Lars Thylen, Makoto Katori, Motoichi Ohtsu

    PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS   471 ( 1 )   162 - 168   2017.4

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1016/j.physa.2016.12.019

    Web of Science

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  • Elliptic Determinantal Processes and Elliptic Dyson Models Reviewed

    Makoto Katori

    SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS   13 ( 1 )   p.079,pp.1-36   2017

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.3842/SIGMA.2017.079

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  • Elliptic Bessel processes and elliptic Dyson models realized as temporally inhomogeneous processes Reviewed

    Makoto Katori

    JOURNAL OF MATHEMATICAL PHYSICS   57 ( 10 )   p.103302,pp.1-32   2016.10

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1063/1.4964253

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  • Bosonic and Fermionic Constructions of Two-Dimensional Quantum Walks

    Hoshiya Yushi, Katori Makoto

    Meeting Abstracts of the Physical Society of Japan   71   2790 - 2790   2016

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    Language：Japanese   Publisher：The Physical Society of Japan  

    DOI： 10.11316/jpsgaiyo.71.2.0_2790

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  • Phase Diagram of Collective Motion of Bacterial Cells in a Shallow Circular Pool Reviewed

    Jun-ichi Wakita, Shota Tsukamoto, Ken Yamamoto, Makoto Katori, Yasuyuki Yamada

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   84 ( 12 )   p.124001,pp.1-6   2015.12

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    DOI： 10.7566/JPSJ.84.124001

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  • Characteristic polynomials of random matrices and noncolliding diffusion processes Invited Reviewed

    Makoto Katori

    RIMS Kokyuroku   1970   22 - 44   2015.11

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  • Self-Elongation with Sequential Folding of a Filament of Bacterial Cells Reviewed

    Ryojiro Honda, Jun-Ichi Wakita, Makoto Katori

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   84 ( 11 )   p.114002,pp.1-7   2015.11

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    DOI： 10.7566/JPSJ.84.114002

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  • Stochastic model showing a transition to self-controlled particle-deposition state induced by optical near-fields Reviewed

    Kan Takahashi, Makoto Katori, Makoto Naruse, Motoichi Ohtsu

    APPLIED PHYSICS B-LASERS AND OPTICS   120 ( 2 )   247 - 254   2015.8

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    DOI： 10.1007/s00340-015-6130-0

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  • Elliptic determinantal process of type A Reviewed

    Makoto Katori

    PROBABILITY THEORY AND RELATED FIELDS   162 ( 3-4 )   637 - 677   2015.8

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    DOI： 10.1007/s00440-014-0581-9

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  • Determinantal Martingales and Correlations of Noncolliding Random Walks Reviewed

    Makoto Katori

    JOURNAL OF STATISTICAL PHYSICS   159 ( 1 )   21 - 42   2015.4

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    DOI： 10.1007/s10955-014-1179-4

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  • 18aCR-3 Stochastic model of photon breeding process using dressed photon

    Takahashi K., Katori M., Naruse M., Kawazoe T., Ohtsu M.

    Meeting Abstracts of the Physical Society of Japan   70   2755 - 2755   2015

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    DOI： 10.11316/jpsgaiyo.70.2.0_2755

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  • Mathematical aspects of the abelian sandpile models

    Makoto Katori

    Meeting Abstracts of the Physical Society of Japan   70   2839 - 2840   2015

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    DOI： 10.11316/jpsgaiyo.70.2.0_2839

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  • 19pCW-7 Analysis of initial growth process of bacteria by nonlinear systems of differential equations

    Honda R., Wakita J., Katori M.

    Meeting Abstracts of the Physical Society of Japan   70   2866 - 2866   2015

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    DOI： 10.11316/jpsgaiyo.70.2.0_2866

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  • 19pCW-8 Phase diagram of collective motions for bacterial cells in a shallow circular pool

    Wakita Jun-ichi, Tsukamoto Shota, Yamamoto Ken, Katori Makoto

    Meeting Abstracts of the Physical Society of Japan   70   2867 - 2867   2015

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    DOI： 10.11316/jpsgaiyo.70.2.0_2867

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  • 24pAJ-4 Stochastic model showing a transition to self-controlled particle-deposition state induced by optical near-fields

    Takahashi K., Katori M., Naruse M., Ohtsu M.

    Meeting Abstracts of the Physical Society of Japan   70   3214 - 3214   2015

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    DOI： 10.11316/jpsgaiyo.70.1.0_3214

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  • Determinantal martingales and noncolliding diffusion processes Reviewed

    Makoto Katori

    STOCHASTIC PROCESSES AND THEIR APPLICATIONS   124 ( 11 )   3724 - 3768   2014.11

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    DOI： 10.1016/j.spa.2014.06.002

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  • Oscillatory matrix model in Chern-Simons theory and Jacobi-theta determinantal point process Reviewed

    Yuta Takahashi, Makoto Katori

    JOURNAL OF MATHEMATICAL PHYSICS   55 ( 9 )   p.093302,pp.1-24   2014.9

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    DOI： 10.1063/1.4894235

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  • Two limiting regimes of interacting Bessel processes Reviewed

    Sergio Andraus, Makoto Katori, Seiji Miyashita

    Journal of Physics A: Mathematical and Theoretical   47 ( 23 )   p.235201,pp.1-30   2014

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    DOI： 10.1088/1751-8113/47/23/235201

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  • Complex Brownian motion representation of the Dyson model Reviewed

    Makoto Katori, Hideki Tanemura

    Electronic Communications in Probability   18 ( 4 )   1 - 16   2013.1

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    DOI： 10.1214/ECP.v18-2554

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  • System of Complex Brownian Motions Associated with the O'Connell Process Reviewed

    Makoto Katori

    JOURNAL OF STATISTICAL PHYSICS   149 ( 3 )   411 - 431   2012.11

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    DOI： 10.1007/s10955-012-0602-y

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  • Interacting particles on the line and Dunkl intertwining operator of type A: application to the freezing regime Reviewed

    Sergio Andraus, Makoto Katori, Seiji Miyashita

    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL   45 ( 39 )   p.395201,pp.1-26   2012.10

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    DOI： 10.1088/1751-8113/45/39/395201

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  • Noncolliding Brownian motion with drift and time-dependent Stieltjes-Wigert determinantal point process Reviewed

    Yuta Takahashi, Makoto Katori

    JOURNAL OF MATHEMATICAL PHYSICS   53 ( 10 )   p.103305   2012.10

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    DOI： 10.1063/1.4758795

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  • Reciprocal Time Relation of Noncolliding Brownian Motion with Drift Reviewed

    Makoto Katori

    JOURNAL OF STATISTICAL PHYSICS   148 ( 1 )   38 - 52   2012.7

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    DOI： 10.1007/s10955-012-0527-5

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  • Survival Probability of Mutually Killing Brownian Motions and the O'Connell Process Reviewed

    Makoto Katori

    JOURNAL OF STATISTICAL PHYSICS   147 ( 1 )   206 - 223   2012.4

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    DOI： 10.1007/s10955-012-0472-3

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  • Determinantal Process Starting from an Orthogonal Symmetry is a Pfaffian Process Reviewed

    Makoto Katori

    JOURNAL OF STATISTICAL PHYSICS   146 ( 2 )   249 - 263   2012.1

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    DOI： 10.1007/s10955-011-0372-y

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  • Noncolliding processes, matrix-valued processes and determinantal processes Invited Reviewed

    Makoto Katori, Hideki Tanemura

    Sugaku Expositions   24 ( 2 )   263 - 289   2011.12

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  • Markov property of determinantal processes with extended sine, Airy, and Bessel kernels Reviewed

    M. Katori, H. Tanemura

    Markov Processes and Related Fields   17 ( 4 )   541 - 580   2011.12

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  • O'Connell's process as a vicious Brownian motion Reviewed

    Makoto Katori

    PHYSICAL REVIEW E   84 ( 6 )   p.061144,pp.1-11   2011.12

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    DOI： 10.1103/PhysRevE.84.061144

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  • Velocity correlations of a discrete-time totally asymmetric simple-exclusion process in stationary state on a circle Reviewed

    Yasuyuki Yamada, Makoto Katori

    PHYSICAL REVIEW E   84 ( 4 )   p.041141,pp.1-8   2011.10

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    DOI： 10.1103/PhysRevE.84.041141

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  • Extreme value distributions of noncolliding diffusion processes Reviewed

    Minami Izumi, Makoto Katori

    RIMS Kokyuroku Bessatsu   B27   45 - 65   2011.8

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  • Fractal Structure of Isothermal Lines and Loops on the Cosmic Microwave Background Reviewed

    Naoki Kobayashi, Yoshihiro Yamazaki, Hiroto Kuninaka, Makoto Katori, Mitsugu Matsushita, Satoki Matsushita, Lung-Yih Chiang

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   80 ( 7 )   p.074003,pp.1-5   2011.7

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    DOI： 10.1143/JPSJ.80.074003

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  • Determinantal correlations of Brownian paths in the plane with nonintersection condition on their loop-erased parts Reviewed

    Makiko Sato, Makoto Katori

    Physical Review E - Statistical, Nonlinear, and Soft Matter Physics   83 ( 4 )   2011.4

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    DOI： 10.1103/PhysRevE.83.041127

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  • Determinantal correlations of Brownian paths in the plane with nonintersection condition on their loop-erased parts Reviewed

    Makiko Sato, Makoto Katori

    PHYSICAL REVIEW E   83 ( 4 )   p.041127,pp.1-12   2011.4

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    DOI： 10.1103/PhysRevE.83.041127

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  • Noncolliding Squared Bessel Processes Reviewed

    Makoto Katori, Hideki Tanemura

    JOURNAL OF STATISTICAL PHYSICS   142 ( 3 )   592 - 615   2011.2

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    DOI： 10.1007/s10955-011-0117-y

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  • Dirac equation with an ultraviolet cutoff and a quantum walk Reviewed

    Fumihito Sato, Makoto Katori

    Physical Review A - Atomic, Molecular, and Optical Physics   81 ( 1 )   2010.1

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    DOI： 10.1103/PhysRevA.81.012314

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  • Non-Equilibrium Dynamics of Dyson&apos;s Model with an Infinite Number of Particles Reviewed

    Makoto Katori, Hideki Tanemura

    COMMUNICATIONS IN MATHEMATICAL PHYSICS   293 ( 2 )   469 - 497   2010.1

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    DOI： 10.1007/s00220-009-0912-3

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  • Dirac equation with an ultraviolet cutoff and a quantum walk Reviewed

    Fumihito Sato, Makoto Katori

    PHYSICAL REVIEW A   81 ( 1 )   p.012314,pp.1-10   2010.1

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    DOI： 10.1103/PhysRevA.81.012314

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  • Zeros of Airy Function and Relaxation Process Reviewed

    Makoto Katori, Hideki Tanemura

    JOURNAL OF STATISTICAL PHYSICS   136 ( 6 )   1177 - 1204   2009.9

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    DOI： 10.1007/s10955-009-9829-7

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  • 非衝突過程・行列値過程・行列式過程 Invited Reviewed

    香取眞理, 種村秀紀

    数学   61 ( 3 )   225 - 247   2009.7

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  • Maximum distributions of bridges of noncolliding Brownian paths Reviewed

    Naoki Kobayashi, Minami Izumi, Makoto Katori

    PHYSICAL REVIEW E   78 ( 5 )   p.051102,pp.1-15   2008.11

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    DOI： 10.1103/PhysRevE.78.051102

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  • Two Bessel bridges conditioned never to collide, double Dirichlet series, and Jacobi theta function Reviewed

    Makoto Katori, Minami Izumi, Naoki Kobayashi

    JOURNAL OF STATISTICAL PHYSICS   131 ( 6 )   1067 - 1083   2008.6

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    DOI： 10.1007/s10955-008-9524-0

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  • Limit distributions of two-dimensional quantum walks Reviewed

    Kyohei Watabe, Naoki Kobayashi, Makoto Katori, Norio Konno

    PHYSICAL REVIEW A   77 ( 6 )   2008.6

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    DOI： 10.1103/PhysRevA.77.062331

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  • Noncolliding Brownian motion and determinantal processes Invited Reviewed

    Makoto Katori, Hideki Tanemura

    JOURNAL OF STATISTICAL PHYSICS   129 ( 5-6 )   1233 - 1277   2007.12

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    DOI： 10.1007/s10955-007-9421-y

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  • Wigner formula of rotation matrices and quantum walks Reviewed

    Takahiro Miyazaki, Makoto Katori, Norio Konno

    Physical Review A - Atomic, Molecular, and Optical Physics   76 ( 1 )   2007.7

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    DOI： 10.1103/PhysRevA.76.012332

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  • Wigner formula of rotation matrices and quantum walks Reviewed

    Takahiro Miyazaki, Makoto Katori, Norio Konno

    PHYSICAL REVIEW A   76 ( 1 )   012332   2007.7

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    DOI： 10.1103/PhysRevA.76.012332

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  • Infinite systems of noncolliding generalized meanders and Riemann-Liouville differintegrals Reviewed

    Makoto Katori, Hideki Tanemura

    PROBABILITY THEORY AND RELATED FIELDS   138 ( 1-2 )   113 - 156   2007.5

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    DOI： 10.1007/s00440-006-0015-4

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  • Quantum walks and orbital states of a Weyl particle (vol 72, pg 012316, 2005) Reviewed

    M Katori, S Fujino, N Konno

    PHYSICAL REVIEW A   72 ( 1 )   12316   2005.7

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    DOI： 10.1103/PhysRevA.72.019904

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  • Quantum walks and orbital states of a Weyl particle Reviewed

    M Katori, S Fujino, N Konno

    PHYSICAL REVIEW A   72 ( 1 )   2005.7

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    DOI： 10.1103/PhysRevA.72.012316

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  • Symmetry of matrix-valued stochastic processes and noncolliding diffusion particle systems Reviewed

    M Katori, H Tanemura

    JOURNAL OF MATHEMATICAL PHYSICS   45 ( 8 )   3058 - 3085   2004.8

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    DOI： 10.1063/1.1765215

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  • Infinite Systems of Non-Colliding Brownian Particles Invited Reviewed

    Makoto Katori, Taro Nagao, Hideki Tanemura

    Advanced Studies in Pure Mathematics,Stochastic Analysis on Large Scale Interacting Systems   39   283 - 306   2004.2

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  • Dualities for the Domany-Kinzel model Reviewed

    M Katori, N Konno, A Sudbury, H Tanemura

    JOURNAL OF THEORETICAL PROBABILITY   17 ( 1 )   131 - 144   2004.1

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    DOI： 10.1023/B:JOTP.0000020478.24536.26

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  • Functional central limit theorems for vicious walkers Reviewed

    Makoto Katori, Hideki Tanemura

    Stochastics and Stochastics Reports   75 ( 6 )   369 - 390   2003.12

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  • Noncolliding Brownian motions and Harish-Chandra formula Reviewed

    Makoto Katori, Hideki Tanemura

    Elect. Comm. in Probab.   8   112 - 121   2003.9

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  • Vicious walks with a wall, noncolliding meanders, and chiral and Bogoliubov-de Gennes random matrices Reviewed

    M Katori, H Tanemura, T Nagao, N Komatsuda

    PHYSICAL REVIEW E   68 ( 2 )   p.021112   2003.8

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    DOI： 10.1103/PhysRevE.68.021112

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  • Moments of vicious walkers and Mobius graph expansions Reviewed

    M Katori, N Komatsuda

    PHYSICAL REVIEW E   67 ( 5 )   p.051110   2003.5

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    DOI： 10.1103/PhysRevE.67.051110

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  • Dynamical correlations among vicious random walkers Reviewed

    T Nagao, M Katori, H Tanemura

    PHYSICS LETTERS A   307 ( 1 )   29 - 35   2003.1

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    DOI： 10.1016/S0375-9601(02)01661-4

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  • Families of vicious walkers Reviewed

    J Cardy, M Katori

    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL   36 ( 3 )   609 - 629   2003.1

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    DOI： 10.1088/0305-4470/36/3/302

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  • Vicious walks with a wall, noncolliding meanders, and chiral and Bogoliubov–de Gennes random matrices Reviewed

    Makoto Katori, Hideki Tanemura, Taro Nagao, Naoaki Komatsuda

    Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics   68 ( 2 )   16   2003

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    DOI： 10.1103/PhysRevE.68.021112

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  • Vicious Walker Model, Schur Function and Random Matrices

    Katori Makoto

    Bulletin of the Japan Society for Industrial and Applied Mathematics   13 ( 4 )   296 - 307   2003

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    We consider the vicious walker model, which was introduced by Michael Fisher in his Boltzmann medal lecture in 1983 as a mathematical model of wetting and melting phenomena. It is a system of particles performing noncolliding random walk in one dimension. Using nonintersecting property of the paths of vicious walkers and by elementary calculus of deter minants, we show that the Green function of the system is equal to the Schur function, which plays an important role in the representation theory of symmetric group, and its two kinds of determinantal expressions are derived. MacMahon conjecture, Bender-Knuth conjecture and Macdonald equality for the summations of Schur functions are discussed from the viewpoint of vicious walker model. By taking the diffusion scaling limit of the vicious walker model, a system of noncolliding Brownian particles is constructed and its relation to the distribution of eigenvalues of real symmetric random matrices is clarified.

    DOI： 10.11540/bjsiam.13.4_296

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  • Moments of vicious walkers and Möbius graph expansions Reviewed

    Makoto Katori, Naoaki Komatsuda

    Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics   67 ( 5 )   10   2003

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    DOI： 10.1103/PhysRevE.67.051110

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  • Scaling limit of vicious walks and two-matrix model Reviewed

    Makoto Katori, Hideki Tanemura

    Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics   66 ( 1 )   2002.7

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    DOI： 10.1103/PhysRevE.66.011105

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  • Scaling limit of vicious walks and two-matrix model Reviewed

    M Katori, H Tanemura

    PHYSICAL REVIEW E   66 ( 1 )   p.011105   2002.7

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    DOI： 10.1103/PhysRevE.66.011105

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  • Limit theorems for the nonattractive Domany-Kinzel model Reviewed

    M Katori, N Konno, H Tanemura

    ANNALS OF PROBABILITY   30 ( 2 )   933 - 947   2002.4

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    DOI： 10.1214/aop/1023481012

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  • Analysis of trajectories of random walkers on spatio-temporal plane Reviewed

    N.Inui, M.Katori

    Trans. Mat. Res. Soc. Jpn.   26   409 - 412   2001.3

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  • Dualities for discrete-time stochastic models in ome dimension Reviewed

    N.Konno, A.Sudbury, H.Tanemura, M.Katori

    Trans. Mat. Res. Soc. Jpn.   26   381 - 384   2001.3

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  • Dependence on direction for spatial distributions for pivotal bonds on percolation \\ Reviewed

    S.Kogure, M.Sekine, M.Katori, N.Konno

    Trans. Mat. Res. Soc. Jpn.   26   369 - 372   2001.3

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  • Analysis of canopy-gap structures of forests by theomal equilibirum correlation equalities Reviewed

    T.Takamatsu, M.Katori

    Trans. Mat. Res. Soc. Jpn.   26   397 - 400   2001.3

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  • On the Drossel-Schwabl limit in a forest fire model Reviewed

    T.Takamatsu, M.Katori

    Trans. Mat. Res. Soc. Jpn.   26   401 - 404   2001.3

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  • Bounds on the critical values of the one-dimensional diffusion contact process Reviewed

    N.Konno, S.Hayashi, A.Sudbury, H.Tanemura, M.Katori

    Trans. Mat. Res. Soc. Jpn.   26   385 - 388   2001.3

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  • Trajectories of two friendly walkers Reviewed

    M.Katori, N.Inui

    Trans. Mat. Res. Soc. Jpn.   26   405 - 407   2001.3

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  • Low-density series expansion for the Domany-Kinzel model Reviewed

    N Inui, M Katori, FM Bhatti

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   70 ( 2 )   359 - 366   2001.2

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    DOI： 10.1143/JPSJ.70.359

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  • Statistical properties of trajectories of friendly walkers on spatio-temporal plane Reviewed

    N Inui, M Katori

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   70 ( 1 )   78 - 85   2001.1

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    DOI： 10.1143/JPSJ.70.78

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  • Fermi partition functions of friendly walkers and pair connectedness of directed percolation Reviewed

    N Inui, M Katori

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   70 ( 1 )   1 - 4   2001.1

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    DOI： 10.1143/JPSJ.70.1

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  • Extenstion of the Arrowsmith-Essam formula to the Domany-Kinzel model Reviewed

    N.Konno, M.Katori

    J. Stat. Phys   101   747 - 774   2000.10

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  • Exact Results for the Abelian Sandpile Models

    KATORI Makoto

    Butsuri   55 ( 4 )   276 - 280   2000.4

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    Language：Japanese   Publisher：The Physical Society of Japan (JPS)  

    DOI： 10.11316/butsuri1946.55.276

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  • Percolation transitions and wetting transitions in stochastic models Invited Reviewed

    M Katori

    BRAZILIAN JOURNAL OF PHYSICS   30 ( 1 )   83 - 96   2000.3

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  • Survival probabilities for discrete-time models in one dimension Reviewed

    M.Katori, N.Konno, H.Tanemura

    J. Stat. Phys.   99   603 - 612   2000.2

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    DOI： 10.1023/A:1018617328216

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  • Proof of breaking of self-organized criticality in a nonconservative Abelian sandpile model Reviewed

    T Tsuchiya, M Katori

    PHYSICAL REVIEW E   61 ( 2 )   1183 - 1188   2000.2

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    DOI： 10.1103/PhysRevE.61.1183

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  • Baxter-Guttmann-Jensen conjecture for power series in directed percolation problem Invited Reviewed

    M.Katori, T.Tsuchiya, N.Inui, H.Kakuno

    Annals of Combinatorics   3   337 - 356   1999.10

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  • Analysis of canopy-gap structures of forests by Ising-Gibbs states - Equilibrium and scaling property of real forests Reviewed

    S Kizaki, M Katori

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   68 ( 8 )   2553 - 2560   1999.8

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    DOI： 10.1143/JPSJ.68.2553

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  • Stochastic lattice model for locust outbreak Reviewed

    Shinya Kizaki, Makoto Katori

    Physica A: Statistical Mechanics and its Applications   266 ( 1-4 )   339 - 342   1999.4

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    DOI： 10.1016/S0378-4371(98)00613-X

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  • Effect of anisotropy on the self-organized critical states of Abelian sandpile models Reviewed

    Tomoko Tsuchiya, Makoto Katori

    Physica A: Statistical Mechanics and its Applications   266 ( 1-4 )   358 - 361   1999.4

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    DOI： 10.1016/S0378-4371(98)00616-5

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  • Exact results for the directed Abelian sandpile models Reviewed

    T Tsuchiya, M Katori

    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL   32 ( 9 )   1629 - 1641   1999.3

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    DOI： 10.1088/0305-4470/32/9/011

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  • Chiral Potts models, friendly walkers and directed percolation problem Reviewed

    T Tsuchiya, M Katori

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   67 ( 5 )   1655 - 1666   1998.5

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    DOI： 10.1143/JPSJ.67.1655

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  • Forest dynamics with canopy gap expansion and stochastic Ising model Reviewed

    M Katori, S Kizaki, Y Terui, T Kubo

    FRACTALS-AN INTERDISCIPLINARY JOURNAL ON THE COMPLEX GEOMETRY OF NATURE   6 ( 1 )   81 - 86   1998.3

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  • n-state exclusive diffusion models for avalanche processes showing self-organized criticality Reviewed

    H Kobayashi, M Katori

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   66 ( 8 )   2367 - 2382   1997.8

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    DOI： 10.1143/JPSJ.66.2367

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  • The number of directed compact site animals and extrapolation formula of directed percolation probability Reviewed

    N Inui, M Katori, G Komatsu, K Kameoka

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   66 ( 5 )   1306 - 1309   1997.5

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    DOI： 10.1143/JPSJ.66.1306

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  • Ballot number representation of the percolation probability series for the directed square lattice Reviewed

    M Katori, N Inui

    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL   30 ( 9 )   2975 - 2994   1997.5

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    DOI： 10.1088/0305-4470/30/9/012

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  • Anomalous heat capacity of antiferromagnet FeBr2 in a magnetic field Reviewed

    HA Katori, K Katsumata, M Katori

    JOURNAL OF APPLIED PHYSICS   81 ( 8 )   4396 - 4398   1997.4

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    DOI： 10.1063/1.364836

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  • Hypergeometric series in a series expansion of the directed-bond percolation probability on the square lattice Reviewed

    M Katori, N Inui, G Komatsu, K Kameoka

    JOURNAL OF STATISTICAL PHYSICS   86 ( 1-2 )   37 - 55   1997.1

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  • Specific-heat anomaly in the Ising antiferromagnet FeBr2 in external magnetic fields Reviewed

    HA Katori, K Katsumata, M Katori

    PHYSICAL REVIEW B   54 ( 14 )   R9620 - R9623   1996.10

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    DOI： 10.1103/PhysRevB.54.R9620

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  • Time-reversal duality and planar lattice duality in non-equilibrium lattice models Reviewed

    M Katori

    FRACTALS-AN INTERDISCIPLINARY JOURNAL ON THE COMPLEX GEOMETRY OF NATURE   4 ( 3 )   285 - 292   1996.9

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    DOI： 10.1142/S0218348X9600039X

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  • Exclusive diffusion model showing self-organized criticality Reviewed

    H Kobayashi, M Katori

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   65 ( 8 )   2536 - 2542   1996.8

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    DOI： 10.1143/JPSJ.65.2536

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  • Mean-field theory of avalanches in self-organized critical states Reviewed

    M Katori, H Kobayashi

    PHYSICA A   229 ( 3-4 )   461 - 477   1996.8

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    DOI： 10.1016/0378-4371(96)00003-9

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  • Catalan numbers in a series expansion of the directed percolation probability on a square lattice Reviewed

    N Inui, M Katori

    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL   29 ( 15 )   4347 - 4364   1996.8

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    DOI： 10.1088/0305-4470/29/15/010

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  • Specific-Heat Anomaly in the Ising Antiferromagnet FeBr2 in External Magnetic Fields

    KATORI H A, KATSUMATA K, KATORI M

    Physical Review B   54 ( 14 )   R9620 - R9623   1996

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  • Specific-heat anomaly in the Ising antiferromagnet F in external magnetic fields Reviewed

    H. Aruga Katori, K. Katsumata, M. Katori

    Physical Review B - Condensed Matter and Materials Physics   54 ( 14 )   R9620 - R9623   1996

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    DOI： 10.1103/PhysRevB.54.R9620

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  • 2-NEIGHBOR STOCHASTIC CELLULAR-AUTOMATA AND THEIR PLANAR LATTICE DUALS Reviewed

    M KATORI, H TSUKAHARA

    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL   28 ( 14 )   3935 - 3957   1995.7

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    DOI： 10.1088/0305-4470/28/14/014

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  • DUALITY AND UNIVERSALITY IN NONEQUILIBRIUM LATTICE MODELS Reviewed

    N INUI, M KATORI, T UZAWA

    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL   28 ( 7 )   1817 - 1830   1995.4

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    DOI： 10.1088/0305-4470/28/7/007

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  • RIGOROUS RESULTS FOR THE DIFFUSIVE CONTACT-PROCESSES IN D-GREATER-THAN-OR-EQUAL-TO-3 Reviewed

    M KATORI

    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL   27 ( 22 )   7327 - 7341   1994.11

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    DOI： 10.1088/0305-4470/27/22/010

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  • STRUCTURAL AND STATISTICAL PROPERTIES OF COMPETING DIRECTED PERCOLATION Reviewed

    S ISOGAMI, M KATORI, M MATSUSHITA

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   63 ( 8 )   2919 - 2929   1994.8

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    DOI： 10.1143/JPSJ.63.2919

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  • REFORMULATION OF GRAYS DUALITY FOR ATTRACTIVE SPIN SYSTEMS AND ITS APPLICATIONS Reviewed

    M KATORI

    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL   27 ( 9 )   3191 - 3211   1994.5

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    DOI： 10.1088/0305-4470/27/9/030

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  • ON THE CAM CANNONICALITY OF THE CLUSTER-VARIATION APPROXIMATIONS Invited Reviewed

    M KATORI, M SUZUKI

    PROGRESS OF THEORETICAL PHYSICS SUPPLEMENT   115 ( 115 )   83 - 93   1994

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  • BOUNDS FOR THE CRITICAL LINE OF THE THETA-CONTACT PROCESSES WITH 1-LESS-THAN-OR-EQUAL-TO-THETA-LESS-THAN-OR-EQUAL-TO-2 Reviewed

    M KATORI, N KONNO

    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL   26 ( 23 )   6597 - 6614   1993.12

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    DOI： 10.1088/0305-4470/26/23/011

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  • ON THE EXTINCTION OF DICKMAN REACTION - DIFFUSION-PROCESSES Reviewed

    M KATORI, N KONNO

    PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS   186 ( 3-4 )   578 - 590   1992.8

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    DOI： 10.1016/0378-4371(92)90218-F

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  • UPPER-BOUNDS FOR ORDER PARAMETERS OF A CLASS OF ATTRACTIVE NEAREST-PARTICLE SYSTEMS WITH FINITE RANGES Reviewed

    N KONNO, M KATORI

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   61 ( 3 )   806 - 811   1992.3

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    DOI： 10.1143/JPSJ.61.806

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  • PHASE-TRANSITIONS IN SPIN SYSTEMS WITHOUT DETAILED BALANCE

    M KATORI, N KONNO

    JOURNAL OF MAGNETISM AND MAGNETIC MATERIALS   104   267 - 268   1992.2

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  • ANALYSIS OF THE ORDER PARAMETER FOR UNIFORM NEAREST PARTICLE SYSTEM Reviewed

    N KONNO, M KATORI

    JOURNAL OF STATISTICAL PHYSICS   65 ( 1-2 )   247 - 254   1991.10

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    DOI： 10.1007/BF01329859

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  • MULTI-EFFECTIVE-FIELD THEORY - APPLICATIONS TO THE CAM ANALYSIS OF THE 2-DIMENSIONAL ISING-MODEL Reviewed

    K MINAMI, Y NONOMURA, M KATORI, M SUZUKI

    PHYSICA A   174 ( 2-3 )   479 - 503   1991.6

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    DOI： 10.1016/0378-4371(91)90344-C

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  • UPPER-BOUNDS FOR SURVIVAL PROBABILITY OF THE CONTACT PROCESS Reviewed

    M KATORI, N KONNO

    JOURNAL OF STATISTICAL PHYSICS   63 ( 1-2 )   115 - 130   1991.4

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    DOI： 10.1007/BF01026595

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  • 3-POINT MARKOV EXTENSION AND AN IMPROVED UPPER BOUND FOR SURVIVAL PROBABILITY OF THE ONE-DIMENSIONAL CONTACT PROCESS Reviewed

    M KATORI, N KONNO

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   60 ( 2 )   418 - 429   1991.2

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    DOI： 10.1143/JPSJ.60.418

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  • APPLICATIONS OF THE HARRIS-FKG INEQUALITY TO UPPER-BOUNDS FOR ORDER PARAMETERS IN THE CONTACT-PROCESSES Reviewed

    N KONNO, M KATORI

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   60 ( 2 )   430 - 434   1991.2

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    DOI： 10.1143/JPSJ.60.430

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  • Correlation Identities for Nearest-Particle Systems and their Applications to One-Dimentional Contact Proces Reviewed

    N.Konno, M.Katori

    Modern Physics Letters   B5 ( 2 )   151 - 159   1991.2

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    DOI： 10.1142/S0217984991000198

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  • AN UPPER BOUND FOR SURVIVAL PROBABILITY OF INFECTED REGION IN THE CONTACT-PROCESSES Reviewed

    M KATORI, N KONNO

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   60 ( 1 )   95 - 99   1991.1

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    DOI： 10.1143/JPSJ.60.95

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  • STUDY OF COHERENT ANOMALIES AND CRITICAL EXPONENTS BASED ON HIGH-LEVEL CLUSTER-VARIATION APPROXIMATIONS Reviewed

    S FUJIKI, M KATORI, M SUZUKI

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   59 ( 8 )   2681 - 2687   1990.8

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    DOI： 10.1143/JPSJ.59.2681

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  • Systematic Approach to Critical Phenomena by the Extended Variational Method and Coherent-Anomaly Method Reviewed

    N.Kawashima, M.Katori, C.Tsallis, M.Suzuki

    International Journal of Modern Physics   B4 ( 7&8 )   1409 - 1422   1990.7

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  • APPLICATIONS OF THE CAM BASED ON A NEW DECOUPLING PROCEDURE OF CORRELATION-FUNCTIONS IN THE ONE-DIMENSIONAL CONTACT PROCESS Reviewed

    N KONNO, M KATORI

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   59 ( 5 )   1581 - 1592   1990.5

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    DOI： 10.1143/JPSJ.59.1581

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  • CORRELATION INEQUALITIES AND LOWER BOUNDS FOR THE CRITICAL VALUE LAMBDA-C OF CONTACT-PROCESSES Reviewed

    M KATORI, N KONNO

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   59 ( 3 )   877 - 887   1990.3

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    DOI： 10.1143/JPSJ.59.877

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  • A 2ND-ORDER PHASE-TRANSITION AS A LIMIT OF THE 1ST-ORDER PHASE-TRANSITIONS - COHERENT ANOMALIES AND CRITICAL PHENOMENA IN THE POTTS MODELS Reviewed

    M KATORI

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   57 ( 12 )   4114 - 4125   1988.12

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    DOI： 10.1143/JPSJ.57.4114

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  • STUDY OF COHERENT ANOMALIES AND CRITICAL EXPONENTS BASED ON THE CLUSTER-VARIATION METHOD Reviewed

    M KATORI, M SUZUKI

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   57 ( 11 )   3753 - 3761   1988.11

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    DOI： 10.1143/JPSJ.57.3753

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  • Coherent-Anomaly Method in Critical Phenomena Reviewed

    M.Katori, M.Suzuki

    Progress in Statistical Mechanics ed. By C. -K.Hu   273 - 287   1988.10

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  • COHERENT-ANOMALY METHOD IN CRITICAL PHENOMENA .5. ESTIMATION OF THE DYNAMICAL CRITICAL EXPONENT-DELTA OF THE TWO-DIMENSIONAL KINETIC ISING-MODEL Reviewed

    M KATORI, M SUZUKI

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   57 ( 3 )   807 - 817   1988.3

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    DOI： 10.1143/JPSJ.57.807

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  • COHERENT-ANOMALY METHOD IN CRITICAL PHENOMENA .3. MEAN-FIELD TRANSFER-MATRIX METHOD IN THE 2D ISING-MODEL Reviewed

    HU, X, M KATORI, M SUZUKI

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   56 ( 11 )   3865 - 3880   1987.11

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    DOI： 10.1143/JPSJ.56.3865

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  • COHERENT ANOMALY METHOD IN CRITICAL PHENOMENA .1.

    M SUZUKI, M KATORI, HU, X

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   56 ( 9 )   3092 - 3112   1987.9

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    DOI： 10.1143/JPSJ.56.3092

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  • COHERENT ANOMALY METHOD IN CRITICAL PHENOMENA .2. APPLICATIONS TO THE TWO-DIMENSIONAL AND 3-DIMENSIONAL ISING-MODELS Reviewed

    M KATORI, M SUZUKI

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   56 ( 9 )   3113 - 3125   1987.9

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    DOI： 10.1143/JPSJ.56.3113

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  • NEW METHOD TO STUDY CRITICAL PHENOMENA - MEAN-FIELD FINITE-SIZE SCALING THEORY Reviewed

    M SUZUKI, M KATORI

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   55 ( 1 )   1 - 4   1986.1

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    DOI： 10.1143/JPSJ.55.1

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  • SCALING LAWS OF THE NONLINEAR PART OF MAGNETIZATION IN THE SK MODEL OF SPIN-GLASSES Reviewed

    M KATORI, M SUZUKI

    PROGRESS OF THEORETICAL PHYSICS   74 ( 6 )   1175 - 1190   1985.12

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    DOI： 10.1143/PTP.74.1175

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Books

  • Elliptic Extensions in Statistical and Stochastic Systems Reviewed

    Makoto Katori（ Role： Sole authorall pages (pp.125)）

    Springer Singapore2  2023.4  （ ISBN:9789811995279 ）

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    Total pages：125   Responsible for pages：125   Language：English   Book type：Scholarly book

    Hermite's theorem makes it known that there are three levels of mathematical frames in which a simple addition formula is valid. They are rational, q-analogue, and elliptic-analogue. Based on the addition formula and associated mathematical structures, productive studies have been carried out in the process of q-extension of the rational (classical) formulas in enumerative combinatorics, theory of special functions, representation theory, study of integrable systems, and so on. Originating from the paper by Date, Jimbo, Kuniba, Miwa, and Okado on the exactly solvable statistical mechanics models using the theta function identities (1987), the formulas obtained at the q-level are now extended to the elliptic level in many research fields in mathematics and theoretical physics. In the present monograph, the recent progress of the elliptic extensions in the study of statistical and stochastic models in equilibrium and nonequilibrium statistical mechanics and probability theory is shown. At the elliptic level, many special functions are used, including Jacobi's theta functions, Weierstrass elliptic functions, Jacobi's elliptic functions, and others. This monograph is not intended to be a handbook of mathematical formulas of these elliptic functions, however. Thus, use is made only of the theta function of a complex-valued argument and a real-valued nome, which is a simplified version of the four kinds of Jacobi's theta functions. Then, the seven systems of orthogonal theta functions, written using a polynomial of the argument multiplied by a single theta function, or pairs of such functions, can be defined. They were introduced by Rosengren and Schlosser (2006), in association with the seven irreducible reduced affine root systems. Using Rosengren and Schlosser's theta functions, non-colliding Brownian bridges on a one-dimensional torus and an interval are discussed, along with determinantal point processes on a two-dimensional torus. Their scaling limits are argued, and the infinite particle systems are derived. Such limit transitions will be regarded as the mathematical realizations of the thermodynamic or hydrodynamic limits that are central subjects of statistical mechanics.

    DOI： 10.1007/978-981-19-9527-9

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  • 例題から展開する熱・統計力学

    香取, 眞理, 森山, 修（ Role： Joint author全文共同執筆）

    サイエンス社  2021.10  （ ISBN:9784781915234 ）

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    Total pages：v, 215p   Language：Japanese   Book type：Textbook, survey, introduction

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  • 例題から展開する電磁気学

    サイエンス社  2018.7 

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  • 例題から展開する力学

    サイエンス社  2017.5 

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  • Progress in Nanophotonics 4, Chapter 2 Nonequilibrium Statistical Mechanical Models for Photon Breeding Processes Assisted by Dressed-Photon-Phonons

    Springer  2017.1 

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  • Progress in Nanophotonics 4, Chapter 2 Nonequilibrium Statistical Mechanical Models for Photon Breeding Processes Assisted by Dressed-Photon-Phonons

    Springer  2017.1 

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  • 詳解と演習 大学院入試問題 「物理学」

    数理工学社  2016.3 

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  • Bessel Processes, Schramm-Loewner Evolution, and the Dyson Model

    Makoto Katori（ Role： Sole author）

    Springer  2015.12 

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  • 統計力学

    裳華房  2010.11 

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  • 問題例で深める物理---統一的思考力を身につけるために---

    サイエンス社  2010.5 

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  • 統計物理学ハンドブック ---熱平衡から非平衡まで---

    朝倉書店  2007.6 

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  • ランダム行列と非衝突過程

    遊星社  2006.8 

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  • 科学技術者のための数学ハンドブック

    朝倉書店  2002.9 

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  • 物理数学の基礎

    サイエンス社  2001.4 

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  • 非平衡統計力学

    裳華房  1999.3 

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  • 複雑系を解く確率モデル(217頁)

    講談社  1997.11 

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  • Coherent-Anomaly Method: Mean-Field, Fluctuations and Systematics(515pages)(Chapter3,Chapter8を執筆)

    World Scientific  1995.7 

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  • Coherent-Anomaly Method: Mean-Field, Fluctuations and Systematics(515pages)(Chapter3,Chapter8)

    World Scientific, Singapore  1995.7 

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MISC

  • ランダム行列とはなにか Invited

    香取 眞理

    数学セミナー   58 ( 2(688) )   8 - 12   2019.2

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    Language：Japanese   Publishing type：Article, review, commentary, editorial, etc. (trade magazine, newspaper, online media)  

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  • Complex systems of dressed photons and applications

    Motoichi Ohtsu, Makoto Katori

    The Review of Laser Engineering   139 - 143   2017.3

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  • Complex System of Dressed Photons and Applications Reviewed

    45 ( 3 )   139 - 143   2017.3

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    Language：Japanese   Publishing type：Article, review, commentary, editorial, etc. (scientific journal)  

    CiNii Books

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  • 新著紹介：小野嘉之著「初歩の統計力学を取り入れた熱力学」

    香取眞理

    日本物理学会誌   72 ( 2 )   p.140   2017.2

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  • Characterization of the hydrodynamic limit of the Dyson model Reviewed

    Sergio Andraus, Makoto Katori

    RIMS Kokyuroku Bessatsu   B59 ( 1 )   157 - 173   2016.7

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  • 偶然を科学する（統計力学と確率論） Invited

    香取眞理

    数理科学   54 (No.634) ( 4 )   30 - 36   2016.4

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  • Abelian Sandpile Models in Statistical Mechanics -- Dissipative Abelian Sandpile Models --

    Makoto Katori

    MI Lecture Note Series   63   58 - 91   2015.8

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  • 10aAR-4 Collective motion of bacterial cells in a two-dimensional circular pool

    Tsukamoto Shota, Yamamoto Ken, Katori Makoto, Wakita Jun-ichi

    Meeting abstracts of the Physical Society of Japan   69 ( 2 )   226 - 226   2014.8

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  • Height correlation of ripped graphene and Lundberg-Folk formula for magnetoresistance Reviewed

    Kazuyuki Gemma, Makoto Katori

    Journal of Institute of Science and Engineering, Chuo University   19 ( 19 )   1 - 21   2014.3

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  • 統計力学と関数論とブラウン運動と

    香取眞理

    数理科学   600 ( 6 )   44 - 49   2013.6

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  • 26pXJ-3 Height correlation of rippled graphene and Lundeberg-Folk formula for magnetoresistance

    Genma Kazuyuki, Katori Makoto

    Meeting abstracts of the Physical Society of Japan   68 ( 1 )   752 - 752   2013.3

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  • 26aXR-6 Monte Carlo simulations of Brownian motion models with Toda-lattice interactions

    Tada Hiroki, Katori Makoto

    Meeting abstracts of the Physical Society of Japan   68 ( 1 )   321 - 321   2013.3

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  • 26pXR-9 Stieltjes-Wigert ensemble and q-Painleve II equation

    Takahashi Yuta, Katori Makoto

    Meeting abstracts of the Physical Society of Japan   68 ( 1 )   335 - 335   2013.3

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  • 26aXR-8 TASEP on a circle and observations of circular motions of bacteria

    Yamada Yasuyuki, Katori Makoto, Wakita Jun-ichi

    Meeting abstracts of the Physical Society of Japan   68 ( 1 )   322 - 322   2013.3

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  • 19pAC-5 Noncolliding Brownian Motion with Drift and Stieltjes-Wigert Ensemble

    Takahashi Yuta, Katori Makoto

    Meeting abstracts of the Physical Society of Japan   67 ( 2 )   269 - 269   2012.8

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  • 26pAC-5 Percolation analysis of the Cosmic Microwave Background radiation

    Higuchi M., Kobayashi N., Wakita J., Yamazaki Y., Kuninaka H., Katori M., Matsushita M., Matsushita S., Chiang Lung-Yih

    Meeting abstracts of the Physical Society of Japan   67 ( 1 )   344 - 344   2012.3

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  • 26pAE-15 Intertwining Operator of Dunkl Processes and Dyson's Model

    Andraus S., Katori M., Miyashita S.

    Meeting abstracts of the Physical Society of Japan   67 ( 1 )   349 - 349   2012.3

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  • 26pAE-13 Power matrix approach for Schramm Loewner Evolution

    Kawahara Yomei, Katori Makoto

    Meeting abstracts of the Physical Society of Japan   67 ( 1 )   349 - 349   2012.3

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  • 26pAE-14 Fractal dimensions and winding angle distributions of random curves

    Nishikiori Yukina, Kobayasi Naoki, Katori Makoto

    Meeting abstracts of the Physical Society of Japan   67 ( 1 )   349 - 349   2012.3

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  • The Calogero-Moser System with Particle Exchange and Dunkl Processes

    ANDRAUS S., 香取眞理, 宮下精二

    日本物理学会講演概要集   67 ( 2 )   2012

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  • 23aGT-12 Cosmic Microwave Background Radiation and Loop Statistics

    Kobayashi Naoki, Yamazaki Yoshihiro, Kuninaka Hiroto, Katori Makoto, Matsushita Mitsugu, Matsushita Satoki, Chiang Lung-Yih

    Meeting abstracts of the Physical Society of Japan   66 ( 2 )   273 - 273   2011.8

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  • 22aGE-12 The velocity correlation function of the totally asymmetric simple exclusion process on a ring and the Gauss hypergeometric function

    Yamada Yasuyuki, Katori Makoto

    Meeting abstracts of the Physical Society of Japan   66 ( 2 )   221 - 221   2011.8

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  • Iterative Schwarz-Christoffel transformations driven by random walks and fractal curves Reviewed

    Fumihito Sato, Makoto Katori

    Journal of the Institute of Science and Engineering Chuo University   16 ( 16 )   1 - 20   2011.5

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  • 26pTC-13 Dunkl Intertwining Operator for the Noncolliding Brownian Motion

    Andraus Sergio, Katori Makoto

    Meeting abstracts of the Physical Society of Japan   66 ( 1 )   313 - 313   2011.3

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  • 28aTB-11 Decomposition formula of the Schutz determinantal correlations in TASEP

    Fukazawa Tomohiro, Katori Makoto

    Meeting abstracts of the Physical Society of Japan   66 ( 1 )   337 - 337   2011.3

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  • 27pTF-1 Fractal structures of statistical ensembles of random loops

    Nishikiori Yukina, Kobayasi Naoki, Katori Makoto

    Meeting abstracts of the Physical Society of Japan   66 ( 1 )   332 - 332   2011.3

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  • 28aTB-10 Nonintersecting Systems of Loop-Erased Brownian Paths in the Plane

    Sato Makiko, Katori Makoto

    Meeting abstracts of the Physical Society of Japan   66 ( 1 )   337 - 337   2011.3

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  • 27pTF-2 Fractal Structure of Isothermal Lines and Loops on the Cosmic Microwave Background

    Kobayashi Naoki, Yamazaki Yoshihiro, Kuninaka Hiroto, Katori Makoto, Matsushita Mitsugu, Matsushita Satoki, Chiang Lung-Yih

    Meeting abstracts of the Physical Society of Japan   66 ( 1 )   333 - 333   2011.3

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  • 28aPS-74 Statistical Analysis for Temperature Fluctuations of Cosmic Microwave Background

    Nakahira R., Higuchi M., Kobayashi N., Kuninaka H., Yamazaki Y., Katori M., Matsushita M., Matsushita S., CHIANG Lung-Yih

    Meeting abstracts of the Physical Society of Japan   66 ( 1 )   364 - 364   2011.3

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  • 24pTH-12 Dunkl Processes and Intertwining Operators

    Andraus Sergio, Katori Makoto

    Meeting abstracts of the Physical Society of Japan   65 ( 2 )   247 - 247   2010.8

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  • 24pTH-9 Formin's determinants and nonintersecting loop-erased walks

    Sato Makiko, Katori Makoto

    Meeting abstracts of the Physical Society of Japan   65 ( 2 )   247 - 247   2010.8

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  • 24pTH-10 Applicaton of Schutz Determinant on Semi-open TASEPs

    Fukazawa Tomohiro, Katori Makoto

    Meeting abstracts of the Physical Society of Japan   65 ( 2 )   247 - 247   2010.8

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  • ランダム行列とその周辺

    香取眞理

    数理科学   48 ( 4 (No.562) )   13 - 19   2010.4

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  • 20aEJ-6 Random Walk-Driven Iterative Schwarz-Christoffel Transfomation

    Sato Fumihito, Katori Makoto

    Meeting abstracts of the Physical Society of Japan   65 ( 1 )   270 - 270   2010.3

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  • ラプラス変換と揺らぎ

    香取眞理

    数理科学   48 ( 3(No.561) )   32 - 37   2010.3

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  • 連載(12)「問題例で深める物理」物理現象の次元性

    香取眞理, 中野徹

    数理科学   48 ( 1 (N0.559) )   59 - 65   2010.1

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  • 連載(11)「問題例で深める物理」流体力学からカオスへ

    香取眞理, 中野徹

    数理科学   47 ( 12 (No.558) )   66 - 71   2009.12

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  • 連載(10)「問題例で深める物理」多体系における集団運動と個別運動

    香取眞理, 中野徹

    数理科学   47 ( 11 (No.557) )   72 - 77   2009.11

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  • 連載(9)「問題例で深める物理」1次元イジング模型と転送行列

    香取眞理, 中野徹

    数理科学   47 ( 10 (No.556) )   72 - 77   2009.10

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  • 連載(8)「問題例で深める物理」変分原理

    香取眞理, 中野徹

    数理科学   47 ( 9 (No.555) )   65 - 70   2009.9

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  • 25aQC-13 Computer simulation of the Schramm-Loewner evolution and its applications

    Sato F., Katori M.

    Meeting abstracts of the Physical Society of Japan   64 ( 2 )   151 - 151   2009.8

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  • 連載(7)「問題例で深める物理」フーリエ級数とフーリエ変換

    香取眞理, 中野徹

    サイエンス社   47 ( 8 (No.554) )   72 - 77   2009.8

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  • 連載(6)「問題例で深める物理」磁場と電場の相対性

    香取眞理, 中野徹

    数理科学   47 ( 7 (No.553) )   72 - 77   2009.7

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  • 連載(5)「問題例で深める物理」マクスウェル方程式の微分形と積分形

    香取眞理, 中野徹

    数理科学   47 ( 6 (No.552) )   66 - 71   2009.6

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  • 連載(4)「問題例で深める物理」二体問題

    香取眞理, 中野徹

    数理科学   47 ( 5 (No.551) )   72 - 77   2009.5

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  • 連載「(3)問題例で深める物理」二項分布からカノニカル分布へ

    香取眞理, 中野徹

    数理科学   47 ( 4 (No.550) )   78 - 83   2009.4

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  • 30pRC-8 Limit Distributions of Quantum Walks and Ultraviolet Cutoff in Dirac Equations

    Sato F., Katori M.

    Meeting abstracts of the Physical Society of Japan   64 ( 1 )   342 - 342   2009.3

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  • 30pRC-6 Extreme Value Distributions of Noncolliding Brownian Paths

    Izumi Minami, Katori Makoto

    Meeting abstracts of the Physical Society of Japan   64 ( 1 )   342 - 342   2009.3

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  • 30pRC-7 One-dimensional quantum random walks and the Gauss hypergeometric functions

    Ootani S., Katori M.

    Meeting abstracts of the Physical Society of Japan   64 ( 1 )   342 - 342   2009.3

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  • 連載(2)「問題例で深める物理」古典力学と量子力学の対応

    香取眞理, 中野徹

    数理科学   47 ( 3 (No.549) )   67 - 72   2009.3

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  • 連載(1)「問題例で深める物理」物理学の縦糸と横糸

    香取眞理, 中野徹

    数理科学   47 ( 2 (No.548) )   72 - 77   2009.2

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  • 「数学のノーベル賞」と統計物理学

    香取眞理

    数理科学   546 ( 12月号 )   5 - 6   2008.12

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  • 21pVC-13 Maximum Distributions of Noncolliding Bessel Bridges I

    Izumi M., Kobayashi N., Katori M.

    Meeting abstracts of the Physical Society of Japan   63 ( 2 )   224 - 224   2008.8

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  • Schramm-Loewner Evolution 入門

    香取眞理

    数理解析研究所講究録   1609   88 - 101   2008.7

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  • 25pPSA-45 Maximum value of the d-dimensional Bessel bridge

    Kobayashi Naoki, Izumi Minami, Katori Makoto

    Meeting abstracts of the Physical Society of Japan   63 ( 1 )   326 - 326   2008.2

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  • 23aWE-1 Large Qudit Limit of One-dimensional Quantum Walks

    Sato M., Katori M.

    Meeting abstracts of the Physical Society of Japan   63 ( 1 )   265 - 265   2008.2

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  • 23aWE-2 Two-Dimensional Quantum Walk Models

    Watabe Kyohei, Katori Makoto

    Meeting abstracts of the Physical Society of Japan   63 ( 1 )   266 - 266   2008.2

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  • 23aWE-3 Two Bessel Bridges Conditioned Never to Collide and Multiple Dirichlet Series

    Izumi M., Kobayashi N., Katori M.

    Meeting abstracts of the Physical Society of Japan   63 ( 1 )   266 - 266   2008.2

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  • 対称性と調和と酔歩と・・・数学ワンダーランドへの誘い、砂田利一著「ダイヤモンドはなぜ美しい？離散調和解析入門」

    香取眞理

    数学セミナー   46 ( no.9/552 )   p.83   2007.9

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  • 臨界現象・フラクタル研究の新世紀--SLE の発見-- Invited Reviewed

    香取眞理

    日本物理学会誌   62 ( 7 )   527 - 531   2007.7

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  • 20aWA-10 Wigner formula of rotation matrices and quantum walks with multi-component qubits

    Miyazaki T., Katori M., Konno N.

    Meeting abstracts of the Physical Society of Japan   62 ( 1 )   278 - 278   2007.2

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  • ランダム行列から無限粒子系の数理へ

    香取眞理

    数理科学2007年2月号   No. 524   42 - 43   2007.2

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  • 土井正男, 統計力学, 朝倉書店, 東京, 2006, viii+227p, 21.5×15.5cm, 本体3,000円, (物理の考え方2), [学部向・大学院向]

    香取 眞理

    日本物理學會誌   61 ( 11 )   851 - 851   2006.11

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  • 新著紹介「統計力学」（土井正男著）

    香取眞理

    日本物理学会誌   61 ( 11 )   p.851   2006.11

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  • 経済物理の偶然と必然

    香取眞理

    数理科学2006年1月号   No.511   14 - 19   2006.1

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  • 物理学辞典（三訂版） Invited Reviewed

    物理学辞典編集委員会

    2005.9

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  • 21pYO-1 Quantum Walks and Weyl Equation

    Katori M., Fujino S., Konno N.

    Meeting abstracts of the Physical Society of Japan   60 ( 2 )   191 - 191   2005.8

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  • 21pYO-2 Orbital States of a Weyl Particle and Limit Theorem of Quantum Walks

    Fujino S., Katori M., Konno N.

    Meeting abstracts of the Physical Society of Japan   60 ( 2 )   191 - 191   2005.8

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  • Nonintersecting paths, noncolliding diffusion processes and representation theory

    Makoto Katori, Hideki Tanemura

    RIMS Kokyuroku   1438   83 - 102   2005.7

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    Other Link： http://hdl.handle.net/2433/47508

  • Non-colliding system of Brownian particles as Pfaffian process

    Makoto Katori

    RIMS Kokyuroku   1422   12 - 25   2005.4

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    Other Link： http://hdl.handle.net/2433/47202

  • 時間的に非斉次な非衝突ブラウン運動

    香取眞理, 種村秀紀

    立教 SFR 講究録 5 「ゲージ理論・行列模型と非平衡統計物理学」   5   36 - 76   2005.2

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  • 27aWM-9 Noncolliding diffusion processes and random matrix theories

    Katori M., Tanemura H.

    Meeting abstracts of the Physical Society of Japan   59 ( 1 )   266 - 266   2004.3

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  • 非衝突乱歩系・シューア関数・ランダム行列 Invited Reviewed

    香取眞理

    応用数理   13 ( 4 )   16 - 27   2003.12

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  • Mobius graphs expansion for moments of vicious walks

    Komatsuda N., Katori M.

    Meeting abstracts of the Physical Society of Japan   58 ( 1 )   297 - 297   2003.3

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  • Infinite systems of non-colliding Brownian particles

    Katori M., Tanemura H.

    Meeting abstracts of the Physical Society of Japan   58 ( 1 )   297 - 297   2003.3

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  • Dynamical correlation functions fbr vicious random walkers

    Nagao Taro, Katori Makoto, Tanemura Hideki

    Meeting abstracts of the Physical Society of Japan   57 ( 2 )   255 - 255   2002.8

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  • Genus expansion formula for moments of vicious walks

    Komatsuda N, Katori M

    Meeting abstracts of the Physical Society of Japan   57 ( 2 )   255 - 255   2002.8

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  • Scaling limit of vicious walks and two-matrix model

    M Katori, Tanemura H

    Meeting abstracts of the Physical Society of Japan   57 ( 2 )   254 - 254   2002.8

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  • Families of vicious walkers

    M Katori, Cardy J

    Meeting abstracts of the Physical Society of Japan   57 ( 2 )   255 - 255   2002.8

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  • Statistical laws in the income of Japanese companies

    T Mizuno, M Katori, H Takayasu, M Takayasu

    EMPIRICAL SCIENCE OF FINANCIAL FLUCTUATIONS   321 - 330   2002

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  • Random walk representation of the directed percolation

    Inui N., Katori M.

    Meeting abstracts of the Physical Society of Japan   56 ( 1 )   220 - 220   2001.3

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  • On the Drossel-Schwabl Limit in a Forest-Fire Model with Aging Trees

    Takamatsu T., Katori M.

    Meeting abstracts of the Physical Society of Japan   56 ( 1 )   219 - 219   2001.3

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  • Stochastic Laws in the Income of Japanese Companies and Randomly Amplified Langevin Equation II

    Mizuno T., Katori M., Takayasu H., Takayasu M.

    Meeting abstracts of the Physical Society of Japan   56 ( 1 )   273 - 273   2001.3

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  • Stochastic Laws in the Income of Japanese Companies and Randomly Amplified Langevin Equation

    Mizuno T., Katori M., Takayasu H., Takayasu M.

    Meeting abstracts of the Physical Society of Japan   55 ( 2 )   202 - 202   2000.9

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  • Statistical properties of the friendly walker

    Inui N., Katori M., Kameoka K.

    Meeting abstracts of the Physical Society of Japan   55 ( 2 )   196 - 196   2000.9

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  • Statistical and Stochastic Laws in the Income of Japanese Companies

    Katori M.

    Meeting abstracts of the Physical Society of Japan   55 ( 2 )   237 - 237   2000.9

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  • Dissipative Abelian Sandpile Models and q=0 Potts Model

    Katori M.

    Meeting abstracts of the Physical Society of Japan   55 ( 2 )   210 - 210   2000.9

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  • Drossel-Schwabl Limit and Self-Organized Criticality in Forest-Fire Model

    Takamatsu T., Katori M.

    Meeting abstracts of the Physical Society of Japan   55 ( 2 )   196 - 196   2000.9

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  • Self-Organized Criticality of Forest-Fire Model with Aging Trees II

    Takamatsu T., Katori M.

    Meeting abstracts of the Physical Society of Japan   55 ( 1 )   211 - 211   2000.3

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  • Extension of the Arrowsmith-Essam Theorem to the Domany-Kinzel Model

    Konno N., Katori M.

    Meeting abstracts of the Physical Society of Japan   55 ( 1 )   203 - 203   2000.3

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  • Percolation and Wetting Transitions in Stochastic Models

    Katori M.

    Meeting abstracts of the Physical Society of Japan   55 ( 1 )   204 - 204   2000.3

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  • Local and Global Survival Probabilities for the Domany-Kinzel Model

    Katori M., Konno N., Tanemura H.

    Meeting abstracts of the Physical Society of Japan   55 ( 1 )   204 - 204   2000.3

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  • Complete Convergence Theorem for the Domany-Kinzel Model

    Katori M., Konno N., Tanemura H.

    Meeting abstracts of the Physical Society of Japan   55 ( 1 )   204 - 204   2000.3

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  • Analysis of Canopy-Gap Structures of Forests by Thermal Equilibrium Correlation Equations

    Takamatsu T., Katori M.

    Meeting abstracts of the Physical Society of Japan   55 ( 1 )   212 - 212   2000.3

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  • J. Marro and R. Dickman, Nonequilibrium Phase Transitions in Lattice Models, Cambridge Univ. Press, Cambridge, 1999, 327+xv, 18×25.3cm, 本体17,820円, (Collection Alea-Sacley Monographs and Texts in Statistical Physics), [大学院向・専門書]

    香取 眞理

    日本物理學會誌   55 ( 2 )   132 - 133   2000.2

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  • 25aT-12 Self-Organized Criticality of Forest-Fire Model with Aging Trees

    TAKAMATSU T, KATORI M

    Meeting abstracts of the Physical Society of Japan   54 ( 2 )   217 - 217   1999.9

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  • 25aT-11 Structure of canopy in forest and surface of a certain random-field

    KIZAKI S, KATORI M

    Meeting abstracts of the Physical Society of Japan   54 ( 2 )   217 - 217   1999.9

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  • 28p-XD-15 Modeling of cooperative phenomena in phase transformation of locusts

    Kizaki S., Katori M.

    Meeting abstracts of the Physical Society of Japan   54 ( 1 )   648 - 648   1999.3

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  • 28p-XF-5 The size-distribution of avalanches for Abelian sandpile models II

    Shimamura M., Tsuchiya T., Katori M.

    Meeting abstracts of the Physical Society of Japan   54 ( 1 )   654 - 654   1999.3

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  • 28p-XF-4 Breaking of Self-Organized Criticality for Nonconservative BTW Models

    Tsuchiya T., Katori M., Shimamura M.

    Meeting abstracts of the Physical Society of Japan   54 ( 1 )   654 - 654   1999.3

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  • 28p-XF-1 Critical behavior of three dimensional directed percolation

    Inui N., Kakuno H., Katori M., Komatsu G., Kameoka K.

    Meeting abstracts of the Physical Society of Japan   54 ( 1 )   653 - 653   1999.3

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  • 北原和夫, 非平衡系の統計力学, 岩波書店, 東京, 1997, xvi+280p., 21.5×15cm, 本体3,500円 (岩波基礎物理シリーズ8) [学部向教科書]

    香取 眞理

    日本物理學會誌   53 ( 10 )   786 - 787   1998.10

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  • 北原和夫「非平衡系の統計力学」

    香取眞理

    日本物理学会誌   53 ( 10 )   786 - 787   1998.10

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  • Exact Solutions Directed Abelian Sandpile Models II

    TSUCHIYA T., KATORI M.

    Meeting abstracts of the Physical Society of Japan   53 ( 2 )   780 - 780   1998.9

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  • Forest Dynamics With Canopy Gap Expansion and Stochastic Ising Model

    KIZAKI S., KATORI M.

    Meeting abstracts of the Physical Society of Japan   53 ( 2 )   779 - 779   1998.9

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  • The size-distribution of avalanches for Abelian sandpile models

    SHIMAMURA M., TSUCHIYA T., KATORI M.

    Meeting abstracts of the Physical Society of Japan   53 ( 2 )   780 - 780   1998.9

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  • ワタリバッタ大発生のシナリオと確率モデル

    香取眞理, 木崎伸也

    Computer Today   85 ( 3 )   10 - 17   1998.5

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  • Exact Solutions for Directed Abelian Sandpile Model

    TSUCHIYA T., KATORI M.

    Meeting abstracts of the Physical Society of Japan   53 ( 1 )   650 - 650   1998.3

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  • 5p-M-7 Generalized sandpile models

    Kobayashi H., Katori M.

    Meeting abstracts of the Physical Society of Japan   52 ( 2 )   888 - 888   1997.9

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  • 6p-YE-14 Generating functions of the interacting random walks and correlation functions of the chiral Potts models

    Tsuchiya T, Katori M

    Meeting abstracts of the Physical Society of Japan   52 ( 2 )   760 - 760   1997.9

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  • 6p-YE-13 Gap distributions in rainforests studied by Ising models

    Katori M, Kizaki S, Terui Y

    Meeting abstracts of the Physical Society of Japan   52 ( 2 )   760 - 760   1997.9

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  • 30p-WE-2 Chiral Potts Model and Directed Percolation II

    Tsuchiya T., Katori M.

    Meeting abstracts of the Physical Society of Japan   52 ( 1 )   725 - 725   1997.3

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  • 30p-WE-1 Chiral Potts Model and Directed Percolation I

    Katori M., Tsuchiya T.

    Meeting abstracts of the Physical Society of Japan   52 ( 1 )   725 - 725   1997.3

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  • The contour method revisited -- Bounds for critical value of directed percolation --

    M.Katori, T.Tsuchiya, N.Satoh, S.Osanai, S.Kizaki

    中央大学理工学部紀要   39 ( 39 )   1 - 13   1997.3

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  • Series expansion for directed percolation and exclusive diffusion model

    M. Katori, H. Kobayashi, N. Inui, G. Komatsu, K. Kameoka

    Journal of the Institute of Science and Engineering, Chuo University   2   15 - 25   1997.3

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  • Mean-field approximations and Monte Carlo simulations for new sandpile models

    Koyayashi H., Katori M.

    Abstracts of the meeting of the Physical Society of Japan. Sectional meeting   1996 ( 3 )   594 - 594   1996.9

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  • Series expansion of asynmmetric directed percolation

    Inui Norio, Katori Makoto, Komatsu Gennichi, Kameoka Kouichi

    Abstracts of the meeting of the Physical Society of Japan. Sectional meeting   1996 ( 3 )   709 - 709   1996.9

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  • Ballot number representation for the series expansion of the directed percolation probability

    Katori M., Inui N.

    Abstracts of the meeting of the Physical Society of Japan. Sectional meeting   1996 ( 3 )   709 - 709   1996.9

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  • 田口善弘「砂時計の七不思議」－粉粒体の動力学－

    香取眞理

    中央評論   215   159 - 160   1996.4

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  • 31a-A-5 Catalan numbers is series expansion of the directed percolation

    Inui N., Katori M.

    Abstracts of the meeting of the Physical Society of Japan. Annual meeting   51 ( 3 )   544 - 544   1996.3

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  • 31a-A-6 Hypergeometric Series in a Series Expansion of the Directed-Bond Percolation Probability on the Square Lattice

    Katori M., Inui N.

    Abstracts of the meeting of the Physical Society of Japan. Annual meeting   51 ( 3 )   545 - 545   1996.3

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  • 31a-A-4 Critical exponent for wedge angle in bond directed percolation

    Tsukahara H., Katori M.

    Abstracts of the meeting of the Physical Society of Japan. Annual meeting   51 ( 3 )   544 - 544   1996.3

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  • Stochastic Cellular Automata and Directed Percolation

    M.Katori, H.Tsukahara, H.Kobayashi

    1   45 - 54   1996.3

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  • Cluster variational approach to non-equilibrium lattice models Invited Reviewed

    M Katori

    THEORY AND APPLICATIONS OF THE CLUSTER VARIATION AND PATH PROBABILITY METHODS   95 - 111   1996

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  • New mean-field approximation for the self-organized critical states in sandpile models

    Kobayashi H., Katori M.

    Abstracts of the meeting of the Physical Society of Japan. Sectional meeting   1995 ( 3 )   689 - 689   1995.9

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  • Spatio-Temporal Directed Percolation and its Continuous-Time Limit

    Tsukahara H., Katori M.

    Abstracts of the meeting of the Physical Society of Japan. Sectional meeting   1995 ( 3 )   731 - 731   1995.9

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  • Two-neighbour stochastic cellular automata and their planar lattice duals

    Katori M., Tsukahara H.

    Abstracts of the meeting of the Physical Society of Japan. Sectional meeting   1995 ( 3 )   731 - 731   1995.9

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  • Cluster approximations for the height distribution in the sandpile model

    Katori M., Kobayashi H.

    Abstracts of the meeting of the Physical Society of Japan. Sectional meeting   1995 ( 3 )   689 - 689   1995.9

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  • 一大学人と漫画

    香取眞理

    中央評論   212   53 - 57   1995.6

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  • 2-dimensional Directed Percolation and its Lattice Dual

    Tsukahara H, Katori M, Inui N

    Abstracts of the meeting of the Physical Society of Japan. Annual meeting   50 ( 3 )   624 - 624   1995.3

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  • Duality and Universality in Nonequilibrium Lattice Models

    Inui N, Katori M, Uzawa T

    Abstracts of the meeting of the Physical Society of Japan. Annual meeting   50 ( 3 )   625 - 625   1995.3

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  • 2p-E-1 Bernoulli property of the infinite totally asymmetric simple exclusion process

    KATORI Makoto

    Abstracts of the meeting of the Physical Society of Japan. Sectional meeting   1994 ( 3 )   444 - 444   1994.8

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  • 楠岡成雄著, 確率と確率過程, 岩波書店, 東京, 1993, x+92p., 21×15cm, 3,600円, 岩波講座応用数学2

    香取 眞理

    日本物理學會誌   49 ( 8 )   674 - 675   1994.8

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  • 楠岡成雄「確率と確率過程」

    香取眞理

    日本物理学会誌   49 ( 8 )   p.674   1994.8

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  • The Holley-Liggett argument revisited : an application to the generalized contact process

    M.Katori, N.Konno

    ICM94 Abstracts   p.149   1994.8

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  • 29p-C-4 Rigorous results fot the diffusive contact processes in d&ge;3

    KATORI Makoto

    Abstracts of the meeting of the Physical Society of Japan. Annual meeting   49 ( 3 )   539 - 539   1994.3

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  • 詳細釣合を満たさない定常分布：コンタクト・プロセスを例にして Invited Reviewed

    香取眞理

    日本物理学会誌   49 ( 2 )   100 - 107   1994.2

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    DOI： 10.11316/butsuri1946.49.100

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  • Phase Transitions in Contact Process and its Related Processes Invited Reviewed

    M.Katori, N.Konno

    Formation, Dynamics and statistics of Patterns ed. By K.Kawasaki and M.Suzuki   2   23 - 72   1993.12

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  • 13p-G-2 On Critical Values of Generalized Contact Processes in One Dimension II

    KATORI Makoto

    Abstracts of the meeting of the Physical Society of Japan. Sectional meeting   1993 ( 3 )   551 - 551   1993.9

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  • 14p-F-11 Structural and Statistical Properties of Directed Percolation

    ISOGAMI Sadao, KATORI Makoto, MATSUSHITA Mitsugu

    Abstracts of the meeting of the Physical Society of Japan. Sectional meeting   1993 ( 3 )   588 - 588   1993.9

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  • 13p-G-3 Existence of Phase Transition in the One-Dimensional Pair Annihilation Model

    KATORI Makoto, KONNO Norio

    Abstracts of the meeting of the Physical Society of Japan. Sectional meeting   1993 ( 3 )   551 - 551   1993.9

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  • 30p-F-8 Asymptotic behavior of diffusive contact process as D →+∞

    Konno Norio, Katori Makoto

    Abstracts of the meeting of the Physical Society of Japan. Annual meeting   48 ( 3 )   502 - 502   1993.3

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  • 27p-ZB-3 A Mean-Field Limit of Localization Transition

    Kawarabayashi T, Katori M, Suzuki M

    1992 ( 3 )   478 - 478   1992.9

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  • 28a-ZA-2 On Critical Values of Generalized Contact Processes in One Dimension

    KATORI Makoto, KONNO Norio

    1992 ( 3 )   514 - 514   1992.9

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  • 28a-ZA-1 Analysis on Critical Values for Diffusive Contact Processes

    KONNO Norio, KATORI Makoto

    1992 ( 3 )   514 - 514   1992.9

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  • 26p-ZB-3 Critical Phenomena of the S=1/2 Heisenberg-Ising Model Studied by CVM and CAM

    Tanaka Giichi, Kimura Minoru, Katori Makoto

    1992 ( 3 )   465 - 465   1992.9

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  • 30a-ZL-13 On Multiparticle Creation Processes

    KATORI Makoto, KONNO Norio

    47 ( 3 )   465 - 465   1992.3

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  • 30a-ZL-12 Bounds on Critical Values for a Class of the Attractive NPSs with Finite Ranges

    KONNO Norio, KATORI Makoto

    47 ( 3 )   464 - 464   1992.3

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  • 27a-ZM-9 A Self- Consistent Approach to Mobility Edge Tranjectories of Localization

    Kawarabayasi T, Katori M, Suzuki M

    47 ( 3 )   387 - 387   1992.3

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  • On Mathematical Models of Reaction-Diffusion Processes on Catalytic Surfaces

    M.Katori, N.Konno

    Pattern Formation in Complex Dissipative Systems ed. By S.Kai   171 - 175   1992.3

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  • On Mathematical Models of Reaction-Diffusion Processes on Catalytic Surfaces

    M.Katori, N.Konno

    Pattern Formation in Complex Dissipative Systems ed. By S.Kai   171 - 175   1992.3

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  • 拡散を伴ったコンタクト・プロセスについて(「非平衡系の統計物理」研究会(その2),研究会報告)

    香取 眞理, 今野 紀雄

    物性研究   59 ( 2 )   175 - 176   1992

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    Other Link： http://hdl.handle.net/2433/94986

  • 触媒表面の数理モデル(基研短期研究会「格子理論の進展-素粒子から生物まで-」,研究会報告)

    香取 眞理, 今野 紀雄

    物性研究   57 ( 6 )   775 - 779   1992

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    Other Link： http://hdl.handle.net/2433/94878

  • 無限粒子系の物理と数学(基研短期研究会『統計物理の現状と展望』～STATPHYS19に向けて～,研究会報告)

    香取 眞理

    物性研究   58 ( 5 )   545 - 552   1992

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    Other Link： http://hdl.handle.net/2433/94920

  • 28p-T-10 On Mathematical Models of Catalytic Surfaces

    KATORI Makoto, KONNO Norio

    46 ( 3 )   446 - 446   1991.9

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  • 28p-BPS-27 A Self-Consistent Approach to Localization in Disordered Electron Systems

    Kawarabayashi T., Katori M., Suzuki M.

    46 ( 3 )   462 - 462   1991.9

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  • 28p-T-11 Analysis of Order Parameter for a Class of the Uniform Nearest Particle Systems

    KONNO Norio, KATORI Makoto

    46 ( 3 )   446 - 446   1991.9

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  • 数学セミナー編集部編数学の最前線

    香取眞理

    日本物理学会誌   46 ( 8 )   p.700 - 700   1991.8

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  • 25p-F-5 Extinction of Branching Random Walk with Pair Annihilation

    KATORI Makoto, KONNO Norio

    1991 ( 3 )   430 - 430   1991.3

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  • セッション「無限粒子系の物理と数学」について(基研研究会「非可逆な多体系への統計物理及びその周辺分野からのアプローチ」報告,研究会報告)

    香取 眞理

    物性研究   57 ( 2 )   215 - 220   1991

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    Other Link： http://dl.ndl.go.jp/info:ndljp/pid/10936748

  • 非可逆な化学反応モデルにおける拡散の効果について(パターン形成、運動と統計,研究会報告)

    香取 眞理, 今野 紀雄

    物性研究   57 ( 3 )   397 - 400   1991

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    Other Link： http://hdl.handle.net/2433/94843

  • An Upper Bound for Survival Probability of Infected Region in the Contact Processes

    Makoto Katori, Norio Konno

    Journal of the Physical Society of Japan   60 ( 1 )   95 - 99   1991

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    DOI： 10.1143/JPSJ.60.95

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  • Phase Transition in Stationary States of Contact Process

    38 ( 2 )   243 - 256   1990.12

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  • 4p-PS-16 Applications of the Harris-FKG inequality to Upper Bounds for Order Parameters in the Contact Processes

    Konno N., Katori M.

    1990 ( 3 )   488 - 488   1990.10

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  • 4p-PS-17 Markov Extension and Upper Bounds for Survival Probability of the One-Dim.Contact Process

    Katori Makoto, Konno Norio

    1990 ( 3 )   488 - 488   1990.10

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  • Upper Bounds on Critical Value in the One-Dimensional Contact Process by a New Decoupling Procedure of Correlation Functions

    N.Konno, M.Katori

    ICM-90 Abstracts   p.164   1990.8

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  • Ta-no-ji approximation and CAM for the two dimensional square lattice

    Fujiki S., Katori M.

    45 ( 3 )   424 - 424   1990.3

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  • Upper and Lower Bounds for the Critical Value λ_c of Contact Process I

    Konno N., Katori M.

    45 ( 3 )   387 - 387   1990.3

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  • Applications of the Multi-Effective Field Theory and CAM to the 2D Ising models

    Minami K., Nonomura Y., Katori M., Suzuki M.

    45 ( 3 )   424 - 424   1990.3

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  • 14.コンタクト・プロセスにおける感染領域の定常分布ついて(「パターン形成、運動及びその統計」研究会,研究会報告)

    香取 眞理, 今野 紀雄

    物性研究   54 ( 4 )   310 - 312   1990

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    Other Link： http://dl.ndl.go.jp/info:ndljp/pid/10935928

  • 5a-R-9 Lower Bounds on the Critical Point in the Contact Process

    Katori M., Konno N.

    1989 ( 3 )   442 - 442   1989.9

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  • 5a-S-9 Applications of the Optimol Multi-Effective Field Theory to the Ising models

    Minami K., Nonomura Y., katori M., Suzuki M.

    1989 ( 3 )   452 - 452   1989.9

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  • 6p-R-7 Classification of stationary measures of 3-state Stochastic Cellular Automata

    Konno N., Katori M.

    1989 ( 3 )   478 - 478   1989.9

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  • C.J.Thompson Classical Equilibrium Statistical Mechanics

    44 ( 8 )   p.612 - 612   1989.8

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  • 28a-TB-5 CAM and The Series of the Approximations based on the Variational Method

    Kawashima N., Katori M., Suzuki M., Tsallis Constantino

    44 ( 3 )   334 - 334   1989.3

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  • 31p-TC-12 Critical Phenomena of Epidemic Models

    Konno N., Katori M.

    44 ( 3 )   426 - 426   1989.3

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  • 31p-TC-11 Systematic Series of Approximations and the CAM Analysis

    Katori Makoto, Konno Norio

    44 ( 3 )   425 - 425   1989.3

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  • 28a-TB-6 On the Cluster Variation Method and CAM Theory

    Fujiki Sumiyoshi, Katori Makoto

    44 ( 3 )   335 - 335   1989.3

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  • 18.Window-CID-CAMによるContact Processの研究(基研研究会「相転移研究の新手法とその応用」,研究会報告)

    香取 真理, 今野 紀雄

    物性研究   51 ( 5 )   465 - 469   1989

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    Other Link： http://hdl.handle.net/2433/93546

  • 2.カノニカル・シリーズの作り方 : クラスター平均場近似と相関等式切断近似(基研研究会「相転移研究の新手法とその応用」,研究会報告)

    香取 真理, 鈴木 増雄

    物性研究   51 ( 5 )   384 - 388   1989

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    Other Link： http://hdl.handle.net/2433/93561

  • 相転移とCAM理論(基研長期研究会「進化の力学への場の理論的アプローチ」,研究会報告)

    香取 真理, 鈴木 増雄

    素粒子論研究   78 ( 2 )   B200 - B204   1988.11

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  • 5p-D5-12 一次転移の極限としての2次転移 : ポッツ模型におけるコヒーレント異常と臨界現象

    香取 真理

    秋の分科会講演予稿集   1988 ( 3 )   407 - 407   1988.9

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  • 5p-D5-10 Contact Processの臨界現象

    今野 紀雄, 香取 眞理

    秋の分科会講演予稿集   1988 ( 3 )   406 - 406   1988.9

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  • 非平衡を捉える一つの視点

    香取眞理

    数理科学   301 ( 7 )   50 - 57   1988.7

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  • 相転移とCAM理論(基研長期研究会「進化の力学への場の理論的アプローチ」報告,研究会報告)

    香取 真理, 鈴木 増雄

    物性研究   51 ( 2 )   236 - 240   1988

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    Other Link： http://hdl.handle.net/2433/93496

  • 26a-X-10 クラスター変分法によるコヒーレント異常と臨界現象の研究 II

    香取 眞理, 鈴木 増雄

    秋の分科会講演予稿集   1987 ( 3 )   316 - 316   1987.9

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  • 26a-X-11 伝送行列を用いたコヒーレント異常法(CAM)とそのイジング模型への応用 III

    胡 暁, 香取 真理, 鈴木 増雄

    秋の分科会講演予稿集   1987 ( 3 )   317 - 317   1987.9

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  • 28a-QC-3 伝送行列を用いたコヒーレント異常法(CAM)とそのイジング模型への応用I

    胡 暁, 香取 真理, 鈴木 増雄

    秋の分科会講演予稿集   1986 ( 3 )   347 - 347   1986.9

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  • 28a-QC-2 コヒーレント異常法(CAM)による動的臨界現象の研究

    香取 眞理, 鈴木 増雄

    秋の分科会講演予稿集   1986 ( 3 )   346 - 346   1986.9

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  • GT線における非線形帯確率について(磁性体における新しいタイプの相転移現象,研究会報告)

    香取 眞理, 鈴木 増雄

    物性研究   46 ( 4 )   558 - 561   1986

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    Other Link： http://dl.ndl.go.jp/info:ndljp/pid/10933559

  • 3a-C-2 2次元・3次元イジング模型における平均場有限サイズスケーリング理論

    香取 眞理, 鈴木 増雄

    秋の分科会講演予稿集   1985 ( 3 )   304 - 304   1985.9

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  • レプリカ理論と非線形帯磁率(A.スピングラスの分子場理論と磁場効果,基研短期研究会「スピングラスとその周辺」,研究会報告)

    香取 真理, 鈴木 増雄

    物性研究   45 ( 2 )   107 - 111   1985

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    スピングラスの研究において,レプリカ理論はその平均場近似として多くの知見を与えている。ここでは,レプリカ理論を解説し,スピングラス相転移に特有な非線形帯磁率の異常について述べる。

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    Other Link： http://hdl.handle.net/2433/91865

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Presentations

  • Non-Hermitian matrix models and non-Hermitian quantum mechanics

    Makoto Katori

    2025.1 

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    Event date： 2025.1 　 　

    Language：Japanese   Presentation type：Oral presentation (general)   Country：Japan  

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  • Non-normality and non-diagonalizability; Open problems of non-Hermitian matrix-valued Brownian motion Invited International conference

    Makoto Katori

    The 22nd symposium "Stochastic Analysis on Large Scale Interacting Systems"  ( Graduate School of Mathematical Sciences, the University of Tokyo )   2024.11  Ryoki Fukushima (University of Tsukuba), Makoto Nakashima (Nagoya University), Makiko Sasada (The University of Tokyo), Kenkichi Tsunoda (Kyushu University)

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    Event date： 2024.11 　 　

    Language：English   Presentation type：Oral presentation (invited, special)   Country：Japan  

    The non-Hermitian matrix-valued Brownian motion (BM)
    is the stochastic process of a random matrix
    whose entries are given by independent complex BMs.
    At each time, the matrix is non-normal and is not
    unitarily diagonalizable.
    In order to diagonalize the matrix, we have to
    construct the similarity transformation
    by determining the left- and right-eigenvectors
    to satisfy the bi-orthonormality relation.
    By It\^o's formula, we have shown such non-normality
    implies that the eigenvalue process
    on $\mathbb{C}$ is coupled with the eigenvector-overlap
    process.
    In other words, the eigenvalue point process on $\mathbb{C}$
    is coupled with other marked point processes
    weighted by the eigenvector-overlaps.
    For such a coupled system, we have considered two approaches.
    One of them is based on the regularized
    Fuglede--Kadison determinant of the matrix.
    This stochastic field should be considered not on
    $\mathbb{C}$ but in $\mathbb{C}^2$.
    Another approach is based on the stochastic
    partial differential equations (SPDEs) for the pairing
    of the (marked) point processes and proper test functions.
    There the SPDEs exhibit a hierarchical structure.
    We also consider the process
    starting from non-diagonalizable matrices.
    In such cases, the Jordan block decomposition becomes
    important and this structure creates
    domains on $\mathbb{C}$, which are called
    the pseudospectra. They are not exact spectra
    but there the resolvent of matrix takes extremely large values.
    Then the coupling between the eigenvalue process
    and the pseudospectrum process should be studied.
    We will report our trials to characterize the
    non-Hermitian matrix-valued BM and
    list out the open problems which have not appeared
    in the previous study on the Hermitian matrix-valued BM
    and its eigenvalue process known as Dyson's BM.
    This talk is based on the joint work with
    Syota Esaki (Oita), Satoshi Yabuoku (Fukuoka)
    (\url{https://arxiv.org/abs/2306.00300}),
    with Jacek Ma{\l}ecki (Wroc{\l}aw),
    and with
    Saori Morimoto (Chuo) and Tomoyuki Shirai (Kyushu)
    (\url{https://arxiv.org/abs/2401.08129}).

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  • Pseudospectrum dynamics in relaxation processes from far-from-normal to near-normal matrices Invited International conference

    Makoto Katori

    Random Operators and Related Topics 2024  ( Tohoku University, Science Complex C, Aoba Science Hall )   2024.11  Fumihiko NAKANO (Tohoku University)

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    Event date： 2024.11 　 　

    Language：English   Presentation type：Oral presentation (invited, special)   Country：Japan  

    We consider nonnormal matrix-valued dynamical systems
    with discrete time.
    For an eigenvalue of matrix,
    the number of times it appears as a root of
    the characteristic polynomial is called the
    algebraic multiplicity.
    On the other hand,
    the geometric multiplicity is the dimensionality
    of the linear space of eigenvectors associated
    with that eigenvalue.
    If the former exceeds the latter,
    then the eigenvalue is defective
    and the matrix becomes nondiagonalizable
    by any similarity transformation.
    The discrete-time of our dynamics is identified with
    the geometric multiplicity of the zero eigenvalue
    $\lambda_0=0$.
    Its algebraic multiplicity
    takes about half of the matrix size at $t=1$
    and increases stepwise in time, which keeps
    excess to the geometric multiplicity until
    their coincidence at the final time.
    We study the relaxation processes from
    far-from-nonnomal to near-normal matrices.
    We show that such processes are well described by
    the dynamics of pseudospectrum
    containing $\lambda_0$,
    whose defectivity is recovering in time.
    Here the pseudospectra are the domains
    on the complex plane which are not necessarily
    exact spectra but in which the resolvent
    of matrix takes extremely large values.
    By constructing generalized eigenspace for
    $\lambda_0$, we give the Jordan block
    decomposition for the resolvent of matrix
    and characterize the pseudospectrum dynamics.
    Separation and dilatation of the symbol curves
    of the corresponding Toeplitz operators are
    observed in the pseudospectrum around $\lambda_0$.
    The matrix-size dependence is also studied.
    We hope that the present study will help
    us to understand the eigenvalue and
    eigenvector-overlap processes
    of non-Hermitian matrix-valued
    stochastic processes started from
    nonnormal and defective matrices.

    \indent This talk is based on the joint work with
    Saori Morimoto (Chuo) and Tomoyuki Shirai (Kyushu)
    (\url{https://arxiv.org/abs/2401.08129}).

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  • Elliptic Extensions in Statistical and Stochastic Systems Invited International conference

    Makoto Katori

    Random Media and Random Fields  ( Leiden University )   2024.8  Lorentz Center

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    Event date： 2024.8 　 　

    Language：English   Presentation type：Oral presentation (invited, special)   Country：Netherlands  

    We will report the recent progress
    of the elliptic extensions in the study of statistical and
    stochastic models in
    equilibrium and nonequilibrium statistical mechanics and
    probability theory.
    We construct two groups of
    interacting particle systems
    using the seven families of
    theta functions with integer labels, which were
    introduced by Rosengren and Schlosser (2006)
    in association with the Macdonald denominators
    (the elliptic extensions of the Weyl denominators)
    of the seven irreducible reduced affine root systems.
    There the integer label indicates
    the total number of particles in each system.
    The first group of systems consists of seven kinds of
    noncolliding Brownian bridges on a circle or an interval,
    and the second one
    of seven kinds of determinantal point processes
    (DPPs) on a two-dimensional torus.
    The former systems are $(1+1)$-dimensional stochastic
    processes and the latter ones are statistical models of
    stationary point configurations in two dimensions,
    both of which provide mathematical models for
    fermion systems with repulsive interactions.
    The boundary conditions
    and the initial/final configurations
    of the noncolliding Brownian bridges,
    and the periodicity conditions of the DPPs are systematically
    changed depending on the choice of
    the root system from the seven types.
    We argue the scaling limits and precisely define
    the infinite particle systems.
    The connections to other statistical systems
    such as the one-component plasma models
    and the Gaussian free fields will be also discussed.
    The present talk is based on a recently published booklet,
    M. Katori: \textit{Elliptic Extensions in Statistical
    and Stochastic Systems},
    SpringerBriefs in Mathematical Physics 47,
    Springer (2023).

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  • Time-evolutionary point processes of eigenvalues weighted by eigenvector-overlaps for the non-Hermitian matrix-valued stochastic processe Invited International coauthorship International conference

    Makoto Katori

    Kyushu Probability Seminar 1 day workshop  ( Nishijin Plaza, Kyushu University )   2024.8  Takuya Murayama, Kohei Noda, Tomoyuki Shirai, Kenkichi Tsunoda (Kyushu University)

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    Event date： 2024.8 　 　

    Language：English   Presentation type：Oral presentation (invited, special)   Country：Japan  

    The non-Hermitian matrix-valued Brownian motion (BM)
    is the stochastic process of a random matrix
    whose entries are given by independent complex BMs.
    We consider a one-parameter extension of this process,
    which can be regarded as a dynamical version
    of Girko's elliptic ensemble interpolating
    the GUE and the Ginibre ensemble of random matrices.
    Notice that the eigenvalue process of GUE is known as
    Dyson's BM.
    For each process in this family,
    the bi-orthogonality relation is imposed between
    the left and the right eigenvector processes, which allows for
    the scale-transformation invariance of the system.
    There each eigenvalue process is coupled with
    the eigenvector-overlap process which is a
    Hermitian matrix-valued process with entries given by
    products of overlaps of the left and the right eigenvectors.
    Time-evolutionary point processes (PPs) of eigenvalues
    and the marked PPs weighted by the elements of
    eigenvector-overlap processes are introduced.
    We study the stochastic equations for the pairings of
    these PPs and proper test functions.
    This talk is based on the joint work with
    Syota Esaki (Oita), Satoshi Yabuoku (Kitakyushu),
    and Jacek Ma{\l}ecki (Wroc{\l}aw).

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  • From Mathematics to Complex Systems

    Makoto Katori

    Mini Symposium on 'Determinantal Point Processes, Quantum Mechanics and Signal Analysis'  ( Korakuen Campus, Chuo University )   2024.7  Department of Phyics, Chuo University

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    Event date： 2024.7 　 　

    Language：English   Presentation type：Oral presentation (keynote)   Country：Japan  

    This workshop is organized on the occasion of having two visitors to Chuo University from abroad, Prof. Z. Mouayn and Prof. L. Wei. The topics will include statistical mechanics, mathematical physics, probability theory, random matrix theory, quantum information theory, and our favorite research subject, complex systems.

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  • Eigenvalues and Pseudospectra in Nonnormal Matrix-Valued Processes Invited International conference

    Makoto Katori

    Random Fields and Processes on Graphs and Fractals  ( Research Institute for Mathematical Sciences, Kyoto University )   2024.6  Yoshihiro Abe (Tohoku University), David Croydon (Kyoto University), Naotaka Kajino (Kyoto University)

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    Event date： 2024.6 　 　

    Language：English   Presentation type：Oral presentation (invited, special)   Country：Japan  

    Motivated by the recent study of the
    non-Hermitian matrix-valued Brownian motion,
    we propose a family of
    matrix-valued dynamical systems generated by
    nonnormal Toeplitz matrices with additive perturbations.
    We first show complicated structures and motions
    of ``eigenvalues'' found in numerical calculations.
    Then we derive the specific equations
    determining the exact-eigenvalue processes.
    Coexistence of exact eigenvalues and pseudospectra
    is clarified by
    comparing the solutions of these equations with
    the numerical results.
    We use the theory of symbol curves of the
    corresponding nonnormal Toeplitz operators
    represented by infinite matrices
    and characterize the numerical results.
    We report a new phenomenon
    such that at each time
    the outermost closed simple curve
    in a symbol curve
    is realized as the exact eigenvalues,
    but the inner part of a symbol curve
    is reduced in size and embedded in
    the complicated structure of the pseudospectrum
    in our process.
    The matrices in our processes are defective
    and the Jordan decompositions
    are studied in connection with
    eigenvector-overlaps.
    The asymptotics of the processes
    in the infinite-matrix limit are
    also reported.
    This talk is based on the joint work
    with Saori Morimoto (Chuo)
    and Tomoyuki Shirai (Kyushu).
    A preprint is available
    at \url{https://arxiv.org/abs/2401.08129}.

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  • Eigenvalues and Pseudospectra in Nonnormal Matrix-Valued Processes Invited International conference

    Makoto Katori

    A Day of Randomness  ( Department of Mathematics, National University of Singapore )   2024.5  Subhro Ghosh (National University of Singapore), Hao Huang (National University of Singapore)

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    Event date： 2024.5 　 　

    Language：English   Presentation type：Oral presentation (invited, special)   Country：Singapore  

    Motivated by a recent study of the
    non-Hermitian matrix-valued Brownian motion
    in random matrix theory,
    we propose a family of
    matrix-valued dynamical systems generated by
    nonnormal Toeplitz matrices with additive perturbations.
    We first show complicated structures and motions
    of ``eigenvalues'' found in numerical calculations.
    Then we derive the specific equations
    determining the exact-eigenvalue processes.
    Coexistence of exact eigenvalues and pseudospectra
    is clarified by
    comparing the solutions of these equations with
    the numerical results.
    We notice that
    there has been an increasing interest in understanding
    the mechanics of pseudospectra
    in many research fields such as
    numerical analysis, semiclassical analysis,
    and mathematical physics.
    We use the theory of symbol curves of the
    corresponding nonnormal Toeplitz operators
    represented by infinite matrices,
    and characterize the numerical results.
    We report a new phenomenon
    such that at each time
    the outermost closed simple curve
    in a symbol curve
    is realized as the exact eigenvalues,
    but the inner part of a symbol curve
    is reduced in size and embedded in
    the complicated structure of the pseudospectrum
    in each process.
    The matrices in our processes are defective,
    that is, non-diagonalizable.
    We study the Jordan decomposition
    of evolving resolvents in connection with
    the generalized eigenvector-overlaps
    to describe the pseduspectrum processes.
    The asymptotics of the processes
    in the infinite-matrix limit are
    also discussed. \\
    \indent This talk is based on the joint work with
    Syota Esaki (Oita) and Satoshi Yabuoku (Kitakyushu)
    (\url{https://arxiv.org/abs/2306.00300}),
    and with
    Saori Morimoto (Chuo) and Tomoyuki Shirai (Kyushu) \\
    (\url{https://arxiv.org/abs/2401.08129}).

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  • Eigenvalue and pseudospectrum processes generated by nonnormal Toeplitz matrices with perturbation Invited International conference

    Makoto Katori

    Random Matrices and Related Topics in Jeju  ( Jeju Island )   2024.5  Sung-Soo Byun (SNU), Nam-Gyu Kang (KIAS), Kyeongsik Nam (KAIST)

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    Event date： 2024.5 　 　

    Language：English   Presentation type：Oral presentation (invited, special)   Country：Korea, Republic of  

    Motivated by the recent study of the
    non-Hermitian matrix-valued Brownian motion
    (Burda et al.: Nucl. Phys. B 897, 421 (2015)),
    we propose two types of
    matrix-valued dynamical processes generated by
    nonnormal Toeplitz matrices with additive perturbations.
    We first show the complicated structures and motions
    of ``eigenvalues'' found in numerical calculations.
    Then we derive the specific equations
    which determine the exact-eigenvalue processes.
    Comparing the solutions of these equations with
    the numerical results,
    coexistence of exact eigenvalues and pseudospectra
    is clarified.
    We characterize the numerical results
    using the notion of symbol curves of the corresponding
    nonnormal Toeplitz operators
    represented by infinite matrices.
    We report a new phenomenon
    in our second model such that at each time
    the outermost closed simple curve
    cut out from the symbol curve
    is realized as exact eigenvalues,
    but the inner part of symbol curve
    is reduced in size and embedded as
    a complicated structure in the pseudospectrum.
    The asymptotics of the processes
    in the infinite-matrix limit are
    also discussed.
    This talk is based on the joint work with Saori Morimoto (Chuo)
    and Tomoyuki Shirai (Kyushu). A preprint is available
    at \url{https://arxiv.org/abs/2401.08129}.

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  • Eigenvalues, eigenvector-overlaps, and pseudospectra of the non-Hermitian matrix-valued stochastic processes Invited International conference

    Makoto Katori

    Probability and Analysis 2024  ( Będlewo )   2024.4  the Nicolaus Copernicus University in Toruń, the University of Warsaw, the University of Wrocław, and the Wrocław University of Science and Technology with the support from the Banach Center

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    Event date： 2024.4 　 　

    Language：English   Presentation type：Oral presentation (invited, special)   Country：Poland  

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  • Eigenvalues, eigenvector-overlaps, and pseudospectra of the non-Hermitian matrix-valued Brownian motion Invited

    Makoto Katori

    2024.1 

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    Event date： 2024.1 　 　

    Language：Japanese   Presentation type：Oral presentation (general)  

    The non-Hermitian matrix-valued Brownian motion
    is the stochastic process of a random matrix
    whose entries are given by independent complex Brownian motions.
    The eigenvector-overlap process is a
    Hermitian matrix-valued process,
    each element of which is given by
    a product of an overlap of right eigenvectors
    and that of left eigenvectors, and
    the square roots of its diagonal elements
    are known as the condition numbers of
    eigenvalues in perturbation theory.
    We derive a set of SDEs
    for the coupled system of the eigenvalue process and the
    eigenvector-overlap process and
    discuss the results from the viewpoint of
    condition numbers.
    The regularized Fuglede--Kadison (FK) determinant
    is introduced which evolves following a stochastic PDE
    on the two-dimensional complex space.
    Time-dependent point process of eigenvalues
    and its variation marked by the squares of
    the condition numbers are
    related to the logarithmic derivatives of the
    FK-determinant random-field.
    We also discuss the pseudospectrum process
    in the case that the initial matrix is nonnormal.
    The present talk is based on the joint works with
    Syota Esaki (Fukuoka) and Satoshi Yabuoku (Kitakyushu)
    (\url{https://arxiv.org/abs/2306.00300})
    and with
    Saori Morimoto (Chuo) and Tomoyuki Shirai (Kyushu).

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  • Eigenvalues and pseudospectra of the non-Hermitian matrix-valued stochastic processes

    Makoto Katori

    2024.1 

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    Event date： 2024.1 　 　

    Language：English   Presentation type：Oral presentation (general)   Country：Japan  

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  • An application of the theory of random point processes; Hyperuniformity of the bushes in deserts Invited

    Makoto Katori

    The 4th meeting of Grant-in-Aid for Transformative Research Areas `Establishing Data Descriptive Science and its Cross-Disciplinary Applications'  2024.1 

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    Event date： 2024.1 　 　

    Language：Japanese   Presentation type：Oral presentation (invited, special)   Country：Japan  

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  • Non-Hermitian matrix-valued Brownian motion and the regularized Fuglede-Kadison determinant random-fields Invited International conference

    Makoto Katori

    Workshop on Random Interacting Systems  ( Institute for Mathematical Sciences, National University of Singapore )   2023.12  Akira Sakai and Rongfeng Sun

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    Event date： 2023.12 　 　

    Language：English   Presentation type：Oral presentation (invited, special)   Country：Singapore  

    The non-Hermitian matrix-valued Brownian motion
    is the stochastic process of a random matrix
    whose entries are given by independent complex Brownian motions.
    The bi-orthogonality relation is imposed between
    the right and the left eigenvector processes, which allows for
    their scale transformations with an invariant eigenvalue process.
    The eigenvector-overlap process is a
    Hermitian matrix-valued process,
    each element of which is given by
    a product of an overlap of right eigenvectors
    and that of left eigenvectors.
    We derive a set of stochastic differential equations (SDEs)
    for the coupled system of the eigenvalue process and the
    eigenvector-overlap process and prove
    the scale-transformation invariance of the obtained SDE system.
    The Fuglede--Kadison (FK) determinant associated with the present
    matrix-valued process is regularized by introducing
    an auxiliary complex variable. This variable is necessary
    to give the stochastic partial differential equations (SPDEs)
    for the time-dependent random field defined by
    the regularized FK determinant
    and for its squared and logarithmic variations.
    Time-dependent point process of eigenvalues
    and its variation weighted by the diagonal elements of
    the eigenvector-overlap process are
    related to the derivatives of the
    logarithmic regularized FK-determinant random-field.
    We also discuss the PDEs obtained by averaging the SPDEs.
    The present talk is based on the joint work with
    Syota Esaki (Fukuoka) and Satoshi Yabuoku (Kitakyushu).
    A preprint is available at \url{https://arxiv.org/abs/2306.00300}.

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  • Non-Hermitian matrix-valued processes and the regularized Fuglede-Kadison determinant random-fields Invited

    Makoto Katori

    Random Operators and Related Topics  ( Hohoku University )   2023.10 

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    Event date： 2023.10 　 　

    Language：English   Presentation type：Oral presentation (invited, special)   Country：Japan  

    We consider a one-parameter family of
    non-Hermitian matrix-valued processes,
    which can be regarded as a dynamical extension
    of Girko's ensemble interpolating
    the GUE and the Ginibre ensemble of random matrices.
    For each process in this family,
    the bi-orthogonality relation is imposed between
    the right and the left eigenvector processes, which allows for
    the scale-transformation invariance of the system.
    There each eigenvalue process is coupled with
    the eigenvector-overlap process, which is a
    Hermitian matrix-valued process with entries given by
    products of overlaps of the right and left eigenvectors.
    The Fuglede--Kadison (FK) determinants of
    the present matrix-valued processes
    are regularized by introducing an auxiliary complex variable.
    Then, associated with the regularized FK determinants,
    the time-dependent random fields
    are defined in the two-dimensional complex space
    and their stochastic partial differential
    equations (SPDEs) are derived.
    Time-dependent point processes of eigenvalues
    and their variations weighted by the diagonal elements of
    the eigenvector-overlap processes are
    related to the logarithmic derivatives of the
    regularized FK-determinant random-fields.
    We also discuss the PDEs obtained by averaging the SPDEs.
    The present talk is based on the joint work with
    Yuya Tanaka, Saori Morimoto, Ayana Ezoe (Chuo),
    Syota Esaki (Fukuoka) and Satoshi Yabuoku (Kitakyushu).

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  • Particle systems for foraging ants and annihilation and creation of paths

    Saori Morimoto, Ayana Ezoe, Yuya Tanaka, Makoto Katori, Hiraku Nishimori

    2023 Annual Meeting of the Japan Society for Mathematical Biology  ( Nara Women's Univarsity )   2023.9  The Japan Society for Mathematical Biology

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    Event date： 2023.9 　 　

    Language：Japanese   Presentation type：Oral presentation (general)   Country：Japan  

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  • Switching particle systems for foraging ants and phase transitions in path selection

    Ayana Ezoe, Saori Morimoto, Yuya Tanaka, Makoto Katori, Hiraku Nishimori

    2023 Annual Meeting of the Japan Society for Mathematical Biology  ( Nara Women's Univarsity )   2023.9  The Japan Society for Mathematical Biology

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    Event date： 2023.9 　 　

    Language：Japanese   Presentation type：Oral presentation (general)   Country：Japan  

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  • Stochastic log-gases, multiple SLEs, and Gaussian free fields Invited International conference

    Makoto Katori

    New trends of conformal theory from probability to gravity  ( Okinawa Institute of Science and Technology (OIST) )   2023.7  Nicolas Delporte, Reiko Toriumi, Shinobu Hikami (OIST)

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    Event date： 2023.7 - 2023.8

    Language：English   Presentation type：Oral presentation (invited, special)   Country：Japan  

    Multiple extensions of Schramm--Loewner evolution (SLE)
    have been usually studied by the method using
    commutation relations of SLEs and the absolute continuity of measures.
    This method is, however, available only in the case such that
    the curves generated by commuting SLEs are separated from each other.
    Recently we have found that this restriction can be removed if
    we impose the coupling between the multiple SLEs and the appropriately
    modified Gaussian free fields (GFFs), where we have followed the
    work by Dub\'edat, Sheffield, Miller, and others on the coupling
    of a single SLE and GFF.
    By It\^o's stochastic calculus, we prove that proper couplings
    between multiple SLEs and GFFs are established if and only if
    the driving processes of multiple SLEs are of
    a specified type of interacting particle systems.
    They are identified with the log-gases extensively studied as
    dynamical extensions of the eigenvalue distributions
    in random matrix ensembles.
    We will show that this new connection between SLE and
    random matrix theory (RMT) enables us to enjoy variety of
    coupled systems due to the variety of ensembles in RMT.
    The law of large numbers are then clarified
    as the Wigner semicircle law and its variations in the RMT level
    and as the Loewner chains driven by
    the processes solving the Burgers-type PDEs
    in the SLE level.
    The present talk is based on the joint work with
    Shinji Koshida (Aalto University).

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  • Elliptic Extensions of Noncolliding Brownian Bridges Invited International conference

    Makoto Katori

    Processes and heat kernels with symmetries (Conference with mini-courses)20  ( Angers, France )   2023.6  Piotr Graczyk (Université d'Angers), Alessandra Occelli (Université d’Angers), Patrice Sawyer (Laurentian University, Sudbury)

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    Event date： 2023.6 　 　

    Language：English   Presentation type：Poster presentation   Country：France  

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  • PDE of the potential field for eigenvalues and eigenvector-overlaps of the non-Hermitian matrix-valued BM International coauthorship International conference

    Yuya TANAKA, Saori MORIMOTO, Ayana EZOE, Makoto KATORI

    Random Matrices and Applications  ( RIMS, Kyoto University )   2023.6  Organaizers: Benoit Collins(Kyoto), Catherine Donati-Martin(Versailles), Noriyoshi Sakuma(Nagoya City), Tomoyuki Shirai(Kyusyu), Ofer Zeitouni(Weizmann Institute of Science)

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    Event date： 2023.6 　 　

    Language：English   Presentation type：Poster presentation   Country：Japan  

    The non-Hermitian matrix-valued Brownian motion (BM) induces
    a coupled system of the eigenvalue process
    and the eigenvector-overlap process.
    Here the eigenvector-overlap process
    is a matrix-valued process, each element of which
    is given by a product of an overlap of right eigenvectors
    and that of left eigenvectors.
    We consider
    the time-dependent random field defined on the two-dimensional
    complex space using the notion of
    the reguralized Fuglede--Kadison determinant
    of the matrix-valued stochastic process.
    As explained in a talk by one of the present authors (MK),
    this random field plays an important role for the system.
    In this presentation, we take average of this random field
    to define a deterministic field and determine the
    partial differential equation (PDE) which this field satisfies.
    We call this field the potential field,
    since its derivatives give
    the time-dependent density functions of the eigenvalue process
    and the eigenvector-overlap process.
    The present consideration will provide a mathematical interpretation
    of the calculus reported in physics literature
    (e.g., Burda et al. (2015)).
    The exact solutions of the PDE
    and explicit expressions for the density functions
    are shown for several initial conditions.
    Comparison with numerical simulations will be
    also reported.

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  • Eienvalues, eigenvector-overlaps, and regularized Fuglede-Kadison determinant of the non-Hermitian matrix-valued Brownian motion Invited International coauthorship International conference

    Makoto Katori

    Random Matrices and Applications  ( RIMS, Kyoto University )   2023.6  Organaizers: Benoit Collins(Kyoto), Catherine Donati-Martin(Versailles), Noriyoshi Sakuma(Nagoya City), Tomoyuki Shirai(Kyusyu), Ofer Zeitouni(Weizmann Institute of Science)

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    Event date： 2023.6 　 　

    Language：English   Presentation type：Oral presentation (invited, special)   Country：Japan  

    The non-Hermitian matrix-valued Brownian motion
    is the stochastic process of a random matrix
    whose entries are given by independent complex Brownian motions.
    The bi-orthogonality relation is imposed between
    the right and the left eigenvector processes, which allows for
    their scale transformations with an invariant eigenvalue process.
    The eigenvector-overlap process is a matrix-valued process,
    each element of which is given by
    a product of an overlap of right eigenvectors
    and that of left eigenvectors.
    We derive a set of stochastic differential equations
    for the coupled system of the eigenvalue process and the
    eigenvector-overlap process and prove
    the scale-transformation invariance of the system.
    The Fuglede--Kadison (FK) determinant associated with the present
    matrix-valued process is regularized by introducing
    an auxiliary complex variable. This variable is necessary
    to give the stochastic partial differential equations (SPDEs)
    for the time-dependent random field associated with
    the regularized FK determinant and for its logarithmic variation.
    Time-dependent point process of eigenvalues
    and its variation weighted by the diagonal elements of
    the eigenvector-overlap process are
    related to the derivatives of the
    logarithmic random-field of the regularized FK determinant.
    From the SPDEs, a system of PDEs
    for the density functions of these two types of
    time-dependent point processes are obtained.
    The present talk is based on the joint work with
    Syota Esaki (Fukuoka) and Satoshi Yabuoku (Kitakyushu).

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  • Elliptic extensions in statistical and stochastic systems Invited International conference

    Makoto Katori

    International Conference on Mathematical Methods in Physics  ( Marrakesh, Morocco )   2023.4  H. Hedenmalm. Z. Mouayn, P. Cerejeiras, S. N. Lagmiri

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    Event date： 2023.4 　 　

    Language：English   Presentation type：Oral presentation (invited, special)   Country：Morocco  

    I will report the recent progress
    of the elliptic extensions in the study of statistical and
    stochastic models in
    equilibrium and nonequilibrium statistical mechanics and
    probability theory $[1]$.
    Using the $R_n$ theta functions $\{\psi^{R_n}_j\}_{j=1}^n$, $n \in \mathbb{N}$
    introduced by Rosengren and Schlosser (2006)
    in association with the seven irreducible reduced affine
    root systems,
    $R_n=A_{n-1}$, $B_n$, $B^{\vee}_n$,
    $C_n$, $C^{\vee}_n$, $BC_n$, $D_n$,
    and their extensions denoted by $\{\Psi^{R_n}_j\}_{j=1}^n, n \in \mathbb{N}$,
    we discuss two groups of
    interacting particle systems, in which $n$ indicates
    the total number of particles in each system
    and $R$ specifies one of the seven types for each model.
    The first group of systems describes
    the noncolliding Brownian bridges
    on a one-dimensional torus $\mathbb{T}$ (\textit{i.e.}, a circle) or an interval,
    and the second one the determinantal point processes
    (DPPs) on a two-dimensional torus $\mathbb{T}^2$.
    The former systems are $(1+1)$-dimensional stochastic processes
    and the latter ones are statistical models of
    stationary point configurations in two dimensions,
    both of which provide mathematical models for
    systems of fermions,
    which are interacting with repulsive forces.
    The boundary conditions
    and the initial/final configurations
    of the noncolliding Brownian bridges,
    and the periodicity conditions of the DPPs are systematically
    changed depending on the choice of $R$ from the seven types.
    We argue the scaling limits
    associated with $n \to \infty$ and precisely define
    the infinite particle systems.
    The connections
    to other statistical systems
    such as the one-component plasma models
    and the Gaussian free fields will be also discussed. \\
    {[1]} Katori, M.: \textit{Elliptic Extensions in Statistical and Stochastic
    Systems}, SpringerBriefs in Mathematical Physics 47,
    Springer (2023).

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  • Stochastic processes on a complex plane associated with non-Hermitian matrix-valued Brownian motions

    Makoto Katori

    2023.1 

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    Event date： 2023.1 　 　

    Language：Japanese   Presentation type：Oral presentation (general)   Country：Japan  

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  • Two-dimensional processes associated with the non-Hermitian matrix-valued Brownian motions Invited

    Makoto Katori

    Workshop on Probabilistic Methods in Statistical Mechanics of Random Media and Random Fields 2023  ( Ni )   2023.1  Japan-Netherlands Research Cooperative Program between JSPS and NWO

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    Event date： 2023.1 　 　

    Language：English   Presentation type：Oral presentation (invited, special)  

    It is well known that the Hermitian matrix-valued Brownian motion (BM),
    H(t), is decoupled into the unitary matrix-valued process
    diagonarlizing H(t) and obtained eigenvalue process.
    The latter process is identified with the Dyson BM with a special
    value of parameter and is realized as the non-colliding BM
    in one dimension.
    It is regarded as the dynamical extension of GUE
    studied in random matrix theory (RMT).
    In the present talk, we discuss the non-Hermitian matrix-valued BM,
    M(t), whose eigenvalues move on the complex plane
    and exhibit a dynamics of the Ginibre ensemble studied in RMT.
    We impose the bi-orthonormality condition between the left- and
    the right-eigenvectors at each time. This means that the
    matrix-valued process diagonalizing M(t) is non-unitary.
    First I will show movies of computer simulations provided by
    my students, Yuya Tanaka, Saori Morimoto, and Ayana Ezoe,
    in order to demonstrate the coupling phenomena
    of the eigenvalue process and the non-unitary matrix-valued
    process for a variety of initial conditions.
    Then I will briefly review the recent results on the SDE
    representation of the processes obtained by Esaki and Yabuoku.
    In contrast with the Dyson BM having the repulsive
    interaction between any pair of particles,
    the eigenvalue process of M(t) is martingale.
    The cross-variations of the eigenvalues define a
    matrix-valued process. It exhibits a time-evolution of
    the overlap matrix whose statistics was
    first studied by Chalker and Mehlig
    for the Ginibre ensemble in RMT.
    We introduce the time-dependent point processes
    of eigenvalues weighted by the values of overlap-matrix elements,
    in addition to the usual eigenvalue point-process.
    Following the electrostatic analogy reported by
    Burda et al. (2015) in physics literature,
    possible hydrodynamic descriptions of these processes
    on the complex plane are shown.

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  • On non-Hermitian matrix-valued Brownian motions Invited

    Makoto Katori

    The 20th Symposium Stochastic Analysis on Large Scale Interacting Systems  ( Nishijin Plaza, Kyushu University )   2022.12 

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    Event date： 2022.12 　 　

    Language：Japanese   Country：Japan  

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  • Multiple Schramm--Loewner evolution and Dyson's Brownian motion model Invited

    Makoto Katori

    Mathematical Society of Japan 2022 Autumn Meeting  ( Hokkaido University )   2022.9  Mathematical Society of Japan

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    Event date： 2022.9 　 　

    Language：Japanese   Presentation type：Oral presentation (invited, special)   Country：Japan  

    Schramm--Loewner evolution (SLE) is a stochastic extension
    of the classical Loewner theory in complex analysis
    on a simply connected proper domain of ${\mathbb{C } }$
    such that the driving function of the Loewner chain of
    conformal maps is given by a one-dimensional stochastic process.
    Here we assume that the domain is the upper-half
    complex-plane ${\mathbb{H } }$ and the driving process runs
    on ${\mathbb{R } }$.
    It was proved that the SLE driven by a time changed Brownian
    motion on ${\mathbb{R } }$, $(B_{\kappa t})_{t \geq 0}$, $\kappa >0$,
    determines a one-parameter family of probability laws
    of a random continuous curve in $\overline{\mathbb{H } }$
    connecting 0 and $\infty$,
    and that this family, denoted by
    SLE$_{\kappa}$, $\kappa >0$, covers all probability laws of such
    curves having the conformal invariance and
    the domain Markov property.
    In probability theory and statistical physics,
    the SLE$_{\kappa}$ has been playing a central role in studying
    critical phenomena associated with continuous phase transitions
    and fractal geometries in two dimensions.
    Therefore, it is natural to generalize the SLE theory to describe
    random multiple curves in ${\mathbb{H } }$ driven by
    an interacting particle system on ${\mathbb{R } }$.
    The problem is that the requirement of the conformal invariance
    and the domain Markov property is not sufficient to determine
    a `canonical' family of multiple SLEs.
    Motivated by the recent work by Sheffield on the
    quantum gravity zipper
    and a series of papers by Miller and Sheffield
    on the imaginary geometry,
    we employ the coupling of Gaussian free fields (GFFs)
    and multiple SLEs.
    We show that
    a multiple SLE is correctly coupled with a certain GFF
    if and only if the driving particle system is
    given by Dyson's Brownian motion model studied
    in random matrix theory.
    Dyson's Brownian motion model is also a one-parameter
    ($\beta>0$) family of one-dimensional log-gases.
    The coupling is achieved if and only if $\beta=8/\kappa$.
    The present study on the GFF/multiple SLE coupling enables
    us to clarify the basic properties of the constructed multiple SLE
    (e.g., continuity of multiple SLE curves,
    `phase transitions' at $\kappa=4$ and 8). Moreover, we expect that
    a notion of conformal invariance of SLE
    will enrich the study of random matrix theory
    via the present results on the trinity of
    the GFF, the multiple SLE, and Dyson's Brownian motion model.
    The present talk is based on a joint work
    with Shinji Koshida (Aalto University).

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  • Random Matrices, Multiple SLE, and Quantum Gravity Invited

    Makoto Katori

    Summer School Mathematical Physics 2022, K. Itô meets M. Sato  ( Graduate School of Mathematical Sciences, the University of Tokyo )   2022.8  Graduate School of Mathematical Sciences, the University of Tokyo, Professor Y. Ogata and Professor Y. Kawahigashi

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    Event date： 2022.8 　 　

    Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech   Country：Japan  

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  • Point processes and multiple-SLE/GFF coupling Invited International conference

    Makoto Katori

    Fourth ZiF Summer School, Randomness in Physics and Mathematics, From Integrable Probability to Disordered Systems  ( ZiF - Zentrum für interdisziplinäre Forschung, Universität Bielefeld, Bielefeld, Germany )   2022.8  ZiF - Zentrum für interdisziplinäre Forschung, Universität Bielefeld, Bielefeld, Germany

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    Event date： 2022.8 　 　

    Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech   Country：Germany  

    (i) a variety of determinantal point processes (DPPs), and
    (ii) the Gaussian analytic functions (GAFs) on a disk and an annulus, and point
    processes given by zeros of the GAFs.
    (iii) the Brownian motion, the Bessel process, the Schramm-Loewner evolution
    (SLE), Dyson’s Brownian motion,
    (iv) the Gaussian free field (GFF) and the coupling between GFF and the multiple
    SLE driven by Dyson’s Brownian motion. Notice that Dyson’s Brownian motion
    with beta=2 can be regarded as a dynamical version of DPP.

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  • Matrix-valued Brownian motions and two-dimensional processes Invited International conference

    Makoto Katori

    Workshop `Crossroad of Statistical Physics and Probability Theory’  ( Korakuen Campus, Chuo University, )   2022.6 

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    Event date： 2022.6 　 　

    Language：Japanese   Presentation type：Oral presentation (invited, special)   Country：Japan  

    I have studied Dyson's Brownian motion model with
    Hideki Tanemura and others, which
    is a Hermitian matrix-valued Brownian motion.
    The eigenvalue process is determinantal in space and time
    and the hydrodynamic limit is described by
    the complex Burgers equation in the inviscid limit.
    In the present talk, I review the recent work by
    Burda et al.~(2015), Grela and Warcho\l~(2018),
    Bourgade and Dubach (2020),
    Akemann et al.~(2020), and others
    on a non-Hermitian matrix-valued Brownian motion.
    I will explain new aspects of its eigenvalue process on the
    complex plane: It is dynamically coupled with
    the left and right eigenvectors and hence
    essentially different from Dyson's process on
    the real line.
    Nevertheless, the inviscid Burgers equation
    and the determinantal structure appear
    associated with the eigenvector processes.
    Some numerical results obtained by my students
    will be also demonstrated.

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  • Random point processes (random matrix theory), random curves (SLE), and random surfaces (quantum gravity) Invited

    Makoto Katori

    9th Meeting of Statistical Physics  ( online )   2022.3  K. Saito (Keio Univ.), H. Tasaki (Gakusyuin Univ.)

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    Event date： 2022.3 　 　

    Language：Japanese   Presentation type：Oral presentation (invited, special)   Country：Japan  

    File： Katori_StatPhys_March2022_v5.pdf

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  • Bosonic fields and fermionic processes Invited International conference

    Makoto Katori

    Workshop on Probabilistic Methods in Statistical Mechanics of Random Media and Random Fields 2022  ( Kyushu University、Ito Campus )   2022.1 

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    Event date： 2022.1 　 　

    Language：Japanese   Presentation type：Oral presentation (invited, special)   Country：Japan  

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  • Gaussian analytic functions and permanental-determinantal point processes on an annulus Invited

    Makoto Katori

    Tokyo Probability Seminar  2021.12 

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    Event date： 2021.12 　 　

    Language：Japanese   Presentation type：Oral presentation (invited, special)   Country：Japan  

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  • Hyperuniformity of the determinantal point processes associated with the Heisenberg group Invited

    Makoto Katori

    Mathematical Aspects of Quantum Fields and Related Topics  ( Kyoto (Zoom) )   2021.12  Research Institute for Mathematical Sciences, Kyoto University

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    Event date： 2021.12 　 　

    Language：Japanese   Presentation type：Oral presentation (invited, special)   Country：Japan  

    The \textit{Ginibre point process} is given by the eigenvalue
    distribution of a non-hermitian complex Gaussian matrix
    in the infinite matrix-size limit.
    This is a \textit{determinantal point process} (DPP) on the complex
    plane $\C$ in the sense that all correlation functions
    are given by determinants specified by an integral
    kernel called the \textit{correlation kernel}.
    As extensions of the Ginibre DPP,
    a one-parameter family of DPPs is defined on
    $\C^d$, in which $d \in \N$ is the parameter
    and the Ginibre DPP is regarded as
    the lowest-dimensional case ($d=1$).
    We call it the \textit{Heisenberg family of DPPs}, and
    we will explain this reason in the first part of the present talk:
    For each $d \in \N$, the correlation kernel is expressed by
    a matrix-element function of the
    \textit{Schr\"{o}dinger representation}
    of the \textit{Heisenberg group}, and is identified with
    the \textit{reproducing kernel}
    of the \textit{Bargmann-Fock space}.
    Then we prove that any DPP in this family has
    \textit{hyperunifomity} as follows:
    We consider a series of bounded domains
    $\Lambda_n \subset \C^d$,
    which are monotonically increasing and
    $\Lambda_n \to \C^d$ as $n \to \infty$.
    They provide a series of `observation windows' to measure
    local density-fluctuation for an infinite point process
    $\Xi$, and then the hyperuniformity is defined by
    \[
    \lim_{n \to \infty} \frac{\var[\Xi(\Lambda_n)]}{\bE[\Xi(\Lambda_n)]}=0.
    \]
    We show that when $\Lambda_n$ are polydisks, the proof is
    readily given by using the \textit{duality relation}
    between DPPs.
    In the case that $\Lambda_n$ are balls, we have derived
    exact formulas of $\var[\Xi(\Lambda_n)]$ using the modified
    Bessel functions, which provide asymptotic expansions
    for $\var[\Xi(\Lambda_n)]$ in $\vol[\Lambda_n] \to \infty$.
    This talk is based on the joint work with
    T. Matsui (Chuo Univ.) and T. Shirai (Kyushu Univ.),
    and with S. Koshida (Aalto Univ.).

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  • Orthogonal theta functions associated with affine root systems and determinantal point processes Invited International conference

    Makoto Katori

    CIRM Conference - Modern Analysis Related to Root Systems with Applications  ( Luminy, Marseille, France (hybrid) )   2021.10  Centre International de Rencontres Mathematiques

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    Event date： 2021.10 　 　

    Language：English   Presentation type：Oral presentation (invited, special)   Country：France  

    Associated with the seven families of irreducible reduced
    affine root systems $R$,
    Rosengren and Schlosser introduced the families of
    $R$-theta functions.
    We consider appropriate inner products and construct
    the orthonormal bases for the Hilbert spaces of $R$-theta functions.
    Using them the reproducing kernels are defined
    and the families of determinantal point processes (DPPs)
    with finite numbers of particles are obtained on a complex plane.
    There the correlation kernels are given by the
    reproducing kernels.
    The double periodicity and symmetry of the DPPs are studied.
    Infinite particle limits provide the Ginibre DPP
    well studied in random matrix theory
    as well as new kinds of infinite DPPs.

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    Other Link： https://www.cirm-math.fr/Schedule/screen_display.php?id_renc=2404

  • Zeros of the i.i.d. Gaussian Laurent series on an annulus Invited International conference

    Makoto Katori

    Stochastic Differential Geometry and Mathematical Physics  ( Rennes (online) )   2021.6  The Henri Lebesgue Center

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    Event date： 2021.6 　 　

    Language：English   Presentation type：Oral presentation (invited, special)   Country：France  

    On an annulus
    ${\mathbb{A } }_q :=\{z \in {\mathbb{C } }: q < |z| < 1\}$
    with a fixed $q \in (0, 1)$,
    we study a Gaussian analytic function (GAF)
    defined by the
    i.i.d.~Gaussian Laurent series.
    The covariance kernel of the GAF is given by
    the weighted Szeg\H{o} kernel of ${\mathbb{A } }_q$
    with the weight parameter $r$
    studied by Mccullough and Shen.
    Conditioning the GAF by giving zeros,
    new GAFs are induced such that
    the covariance kernels are also given by
    the weighted Szeg\H{o} kernel of Mccullough and Shen
    but the weight parameter $r$
    is changed depending on the given zeros.
    We prove that the zero set of the GAF provides
    a permanental-determinantal point process (PDPP)
    in which each correlation function is expressed by
    a permanent multiplied by a determinant.
    If we take the limit $q \to 0$,
    a simpler but still non-trivial
    PDPP is obtained on a punctured unit disk
    ${\mathbb{D } }^{\times} := {\mathbb{D } } \setminus \{0\}$.
    In the further limit $r \to 0$
    the present PDPP is reduced to the
    determinantal point process on ${\mathbb{D } }$ studied by
    Peres and Vir\'ag.
    The present talk is based on
    a joint work with Tomoyuki Shirai
    (https://arxiv.org/abs/2008.04177).

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  • Complex Burgers equations for log-gases and free convolutions Invited

    Makoto Katori

    Workshop on `Random matrices, Determinantal point processes and Gaussian analytic functions'  ( online )   2021.3  Kyushu University, Institute of Math for Industry

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    Event date： 2021.3 　 　

    Language：Japanese   Presentation type：Oral presentation (invited, special)   Country：Japan  

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  • Gaussian analytic function with the Szego kernel on an annulus and its zeros Invited

    Makoto Katori

    Department of Mathematics Colloquium, Kyoto University  ( online )   2020.10  Department of Mathematics, Kyoto University

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    Event date： 2020.10 　 　

    Language：Japanese   Presentation type：Oral presentation (invited, special)   Country：Japan  

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  • Elliptic extensions of determinantal point processes Invited

    Makoto Katori

    Mathematical Society of Japan, Autumn Meeting  ( Kumamoto University (online) )   2020.9  Mathematical Society of Japan

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    Event date： 2020.9 　 　

    Language：Japanese   Presentation type：Oral presentation (invited, special)   Country：Japan  

    A point process is a statistical ensemble of
    random nonnegative-integer-valued Radon measures
    on a space equipped with a reference measure.
    We consider the case in which for any integer $n$
    an $n$-point correlation function is well defined
    with respect to the $n$-product of reference measure.
    When an $n$-point correlation function is given by
    a determinant of $n \times n$ matrix for every $n$
    and the entries of matrices are
    determined by a kernel of an integral operator,
    the point process is said to be determinantal
    and the kernel is called the correlation kernel.
    Many examples of determinantal point processes (DPPs)
    have been studied in random matrix theory and correlation
    kernels provide reproducing kernels
    which construct reproducing kernel Hilbert spaces.
    Recently we are interested in the DPPs
    in which correlation kernels are expressed using
    Jacobi's theta functions and Weierstrass' elliptic functions.
    In the present talk we will explain that
    these new examples of DPPs can be regarded as
    elliptic extensions of the classical DPPs and their
    $q$-extensions (trigonometric extensions).
    In particular we will report an elliptic extension of the
    beautiful work by Peres and Vir\'ag published in 2005,
    who considered the Gaussian analytic function (GAF)
    on a unit disk ${\mathbb{D } }$ defined as
    an ensemble of random power series with i.i.d.~complex
    Gaussian coefficients.
    There the covariance kernel of GAF is
    given by the reproducing kernel of the Hardy space on
    ${\mathbb{D } }$ called the Szeg\H{o} kernel of ${\mathbb{D } }$.
    They showed that zeros of the GAF form a DPP whose
    correlation kernel is equal to the Bergman kernel
    of ${\mathbb{D } }$.
    This talk is based on the joint work with Tomoyuki Shirai
    (IMI, Kyushu University).

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  • Determinantal Point Processes, Stochastic Log-Gases, and Beyond Invited International conference

    Makoto Katori

    Workshop `Probability and Stochastic Processes’  ( Orange County, Coorg )   2020.2  the Indian Academy of Sciences

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    Event date： 2020.2 　 　

    Language：English   Presentation type：Oral presentation (invited, special)   Country：India  

    A determinantal point process (DPP) is an ensemble
    of random nonnegative-integer-valued Radon measures,
    whose correlation functions are all given by determinants
    specified by an integral kernel called the correlation kernel.
    First we show our new scheme of DPPs in which
    a notion of partial isometies between a pair of Hilbert spaces
    plays an important role.
    Many examples of DPPs in one-, two-, and higher-dimensional
    spaces are demonstrated, where several types
    of weak convergence from finite DPPs to
    infinite DPPs are given.
    Dynamical extensions of DPP are realized in one-dimensional
    systems of diffusive particles conditioned
    never to collide with each other.
    They are regarded as one-dimensional stochastic log-gases,
    or the two-dimensional Coulomb gases
    confined in one-dimensional spaces.
    In the second section, we consider such
    interacting particle systems in one dimension.
    We introduce a notion of
    determinantal martingale and prove that,
    if the system has determinantal martingale representation (DMR),
    then it is a determinantal stochastic process (DSP) in the sense that
    all spatio-temporal correlation function are expressed by
    a determinant.
    In the last section, we construct processes of
    Gaussian free fields (GFFs) on simply connected
    proper subdomains of $\C$ coupled with
    interacting particle systems defined
    on boundaries of the domains.
    There we use multiple Schramm--Loewner evolutions (SLEs)
    driven by the interacting particle systems.
    We prove that, if the driving processes
    are time-changes of the log-gases studied in the
    second section, then the obtained GFF with multiple SLEs
    are stationary.
    The stationarity defines an equivalence relation of
    GFFs, which will be regarded as a generalization of
    the imaginary surface studied by Miller and Sheffield.

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  • Correlation kernels of determinantal point processes expressed by Jacobi theta functions

    Makoto Katori

    2020.1 

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    Event date： 2020.1 　 　

    Language：Japanese   Presentation type：Oral presentation (general)   Country：Japan  

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  • Zeros of Gaussian analytic functions in the annulus and hyperdeterminantal point processes Invited

    KATORI Makoto

    Spectra of Random Operators and Related Topics  ( Gakushuin University )   2020.1 

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  • Gaussian free fields coupled with stochastic log-gases via multiple SLEs Invited

    KATORI Makoto

    Stochastic Analysis on Particle Systems  ( Keio University, Hiyoshi Campus )   2019.12 

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  • Zeros of the i.i.d. Gaussian Laurent series in the annulus Invited

    KATORI Makoto

    The 18th Symposium `Stochastic Analysis on Large Scale Interacting Systems'  ( Department of Mathematics, Osaka University )   2019.11 

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    Language：Japanese   Presentation type：Oral presentation (invited, special)  

    File： schedule.pdf

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  • Partial isometries, duality, and determinantal point processes Invited International conference

    KATORI Makoto

    Japanese-German Open Conference on Stochastic Analysis 2019  ( Fukuoka University )   2019.9  Japanese-German Open Conference

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    Language：English   Presentation type：Oral presentation (invited, special)  

    A determinantal point process (DPP) is
    an ensemble of random nonnegative-integer-valued
    Radon measures $\Xi$ on
    a space $S$ with measure $\lambda$,
    whose correlation functions are all
    given by determinants specified by an
    integral kernel $K$ called the correlation kernel.
    We consider a pair of Hilbert spaces,
    $H_{\ell}, \ell=1,2$, which are assumed to
    be realized as $L^2$-spaces,
    $L^2(S_{\ell}, \lambda_{\ell})$, $\ell=1,2$,
    and introduce
    a bounded linear operator ${\cal W} : H_1 \to H_2$
    and its adjoint ${\cal W}^{\ast} : H_2 \to H_1$.
    We prove that if both of ${\cal W}$ and ${\cal W}^{\ast}$ are
    partial isometries and both of ${\cal W}^{\ast} {\cal W}$ and
    ${\cal W} {\cal W}^{\ast}$
    are of locally trace class, then we have unique pair
    of DPPs, $(\Xi_{\ell}, K_{\ell}, \lambda_{\ell})$, $\ell=1,2$,
    which satisfy useful duality relations.
    We assume that ${\cal W}$ admits an integral kernel $W$
    on $L^2(S_1, \lambda_1)$,
    and give practical setting of $W$ which makes
    ${\cal W}$ and ${\cal W}^{\ast}$ satisfy the above conditions.
    By showing several examples,
    we demonstrate that the class of DPPs
    obtained by our method is large enough to
    study universal structures of DPPs.
    The present talk is based on
    a joint work with Tomoyuki Shirai
    (https://arxiv.org/abs/1903.04945).

    File： JpGerTimeTable0819.pdf

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  • Determinantal point processes in two-dimensional and higher-dimensional spaces Invited International conference

    KATORI Makoto

    Interactions between commutative and non-commutative probability, JSPS Program of France-Japan Bilateral Joint Seminars  ( Faculty of Science, Kyoto University )   2019.8  the JSPS Program of France-Japan Bilateral Joint Seminar

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    Language：English   Presentation type：Oral presentation (invited, special)  

    First I will explain a general framework of determinantal
    point processes (DPPs) based on the notions of
    partial isometries of Hilbert spaces
    and orthonormal functions.
    As examples of DPPs constructed by this framework,
    several kinds of DPPs are discussed in the two-dimensional
    spaces (e.g., a complex plane, a torus, a cylinder, and a sphere)
    as well as in higher-dimensional spaces.
    Universal properties observed in the bulk scaling limit
    are shown. Systems of stochastic differential equations
    having these DPPs as invariant measures are discussed.
    The present talk is based on the paper
    to be published in Commun. Math. Phys.
    (https://doi.org/10.1007/s00220-019-03351-5)
    and on a joint work with Tomoyuki Shirai
    (https://arxiv.org/abs/1903.04945).

    File： JFprogram.pdf

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  • Gaussian Free Fields with Boundary Points, Multiple SLEs, and Log-Gases Invited International conference

    KATORI Makoto

    The 12th Mathematical Society of Japan, Seasonal Institute (MSJ-SI) `Stochastic Analysis, Random Fields and Integrable Probability’  ( Kyushu University )   2019.8  Mathematical Society of Japan

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    Language：English   Presentation type：Oral presentation (invited, special)  

    A quantum surface (QS) (resp. an imaginary surface (IS)) is
    an equivalence class of pairs of simply commenced domains
    $D \subsetneq {\mathbb{C } }$ and the Gaussian free fields (GFFs) on $D$
    with the free (resp. Dirichlet) boundary condition
    induced by the conformal equivalence for random metric spaces.
    We define a QS with $N+1$ marked boundary points (MBPs)
    and an IS with $N+1$ boundary condition changing points (BCCPs)
    on $\partial D$ with $N \in {\mathbb{Z } }_{\geq 1}$, in which
    the real (resp. imaginary) part of the sum of ${\mathbb{C } }$-valued
    logarithmic (2D Coulomb) potentials arising from the MBPs (resp. BCCPs)
    is added to GFF in $D$.
    We consider the situation such that the boundary points evolve in time
    as a stochastic log-gas on $\partial D$ and
    multiple random slits are generated in $D$ by the
    multiple Schramm--Loewner evolution (SLE) driven by
    that stochastic log-gas.
    Then we cut the domain $D$ along the SLE slits, restrict the GFF
    on the resulting domain, and pull it back to $D$ following
    the reverse flow of the multiple SLE.
    We prove that if the log-gases on $\partial D$ follow
    the stochastic differential equations well-studied
    in random matrix theory ({\it e.g.}, Dyson's Brownian
    motion model, the Bru--Wishart processes),
    and parameters are properly chosen,
    then the coupled systems of GFFs and multiple SLE slits
    provide stationary processes.
    The obtained random systems are used to solve
    interesting geometric problems called
    the conformal welding problem and the flow line problem.
    The present study extends the previous
    results for a QS with two MBPs reported by Sheffield
    and for an IS with two BCCPs by Miller and Sheffield.
    This is a joint work with Shinji Koshida (Chuo University);
    see https://arxiv.org/abs/1903.09925.

    File： MSJ-SIprogram.pdf

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  • Quantum surface with marked boundary points and multiple SLE driven by Dyson model Invited International conference

    KATORI Makoto

    Japan Netherlands Workshop: Probabilistic Methods in Statistical Mechanics of Random Media  ( Lorentz Center, Leiden University )   2019.5  Mathematical Institute, Leiden University

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    Language：English   Presentation type：Oral presentation (invited, special)  

    File： Japan_Netherlands_May2019.pdf

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  • Partial Isometries, Duality, and Determinantal Point Processes Invited International conference

    KATORI Makoto

    Workshop on Random Matrices, Stochastic Geometry and Related Topics  ( National University of Singapore (NUS )   2019.3  National University of Singapore (NUS

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    Language：English   Presentation type：Oral presentation (invited, special)  

    A determinantal point process (DPP) is
    an ensemble of random $\mathbb{Z}_{\geq 0}$-valued
    Radon measures $\Xi$ on
    a space $S$ with measure $\lambda$,
    whose correlation functions are all
    given by determinants specified by an
    integral kernel $K$ called the correlation kernel.
    We consider a pair of Hilbert spaces,
    $H_{\ell}, \ell=1,2$, which are assumed to
    be realized as $L^2$-spaces,
    $L^2(S_{\ell}, \lambda_{\ell})$, $\ell=1,2$,
    and introduce
    a linear operator ${\cal W} : H_1 \mapsto H_2$
    and its adjoint ${\cal W}^{\ast} : H_2 \mapsto H_1$.
    We prove that if both of ${\cal W}$ and ${\cal W}^{\ast}$ are
    partial isometries and both of ${\cal W}^{\ast} {\cal W}$ and
    ${\cal W} {\cal W}^{\ast}$
    are of locally trace class, then we have unique pair
    of DPPs, $(\Xi_{\ell}, K_{\ell}, \lambda_{\ell})$, $\ell=1,2$,
    which satisfy duality relations.
    We assume that ${\cal W}$ admits an integral kernel $W$
    on $L^2(S_1, \lambda_1)$,
    and give practical setting of $W$ which makes
    ${\cal W}$ and ${\cal W}^{\ast}$ satisfy the above conditions.
    In order to demonstrate that the class of DPPs
    obtained by our method is large enough to
    study universal structures in a variety of DPPs,
    we show many examples of DPPs
    in one-, two-, and higher-dimensional spaces $S$,
    where several types of weak convergence from finite DPPs
    to infinite DPPs are given.
    One-parameter ($d \in \mathbb{Z}_{\geq 1}$) series of DPPs
    on $S=\mathbb{R}^d$ and $\mathbb{C}^d$ are discussed,
    which we call the Euclidean and the Heisenberg
    families of infinite DPPs, respectively, following
    the terminologies of Zelditch.
    This is a joint work with Tomoyuki Shirai.

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  • Universality of Determinantal Point Processes on Riemannian Manifolds Invited

    KATORI Makoto

    ( Shizuoka University, Department of Science )   2019.3  Shizuoka University, Department of Scence

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    Language：Japanese   Presentation type：Oral presentation (invited, special)  

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  • Determinantal point processes in high-dimensional spaces

    KATORI Makoto

    ( Nara Women's University, Department of Mathematics )   2019.1  Nara Women's University, Department of Mathematics

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  • Determinantal point processes on planes, tori, and spheres Invited International conference

    KATORI Makoto

    Spectra of Random Operators and Related Topics  ( Graduate School of Human and Environmental Studies, Kyoto University )   2019.1  Graduate School of Human and Environmental Studies, Kyoto University

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  • Elliptic DPP, one-component plasma, and GFF Invited International conference

    Makoto Katori

    RIMS Research Project `Gaussian Free Fields and Related Topics'  ( Research Institute for Mathematical Sciences (RIMS), Kyoto University )   2018.9  Research Institute for Mathematical Sciences (RIMS), Kyoto University

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    We introduce new families of determinantal point processes (DPPs)
    on a complex plane ${\mathbb{C } }$, which are classified into seven types
    following the irreducible reduced affine root systems,
    $R_N=A_N$, $B_N$, $B^{\vee}_N$, $C_N$, $C^{\vee}_N$, $BC_N$, $D_N$,
    $N \in {\mathbb{N } }$.
    Their multivariate probability densities are totally elliptic functions
    with periods $(L, iW)$, $0 < L, W < \infty$, $i=\sqrt{-1}$.
    The construction is based on the orthogonality relations
    with respect to the double integrals over the fundamental domain,
    $[0, L) \times [0, iW)$, which are proved in this paper
    for the $R_N$-theta functions introduced by Rosengren and Schlosser.
    In the scaling limit $N \to \infty, L \to \infty$
    with constant density
    $\rho=N/(LW)$ and constant $W$, we obtain four types of
    DPPs with an infinite number of
    points on ${\mathbb{C } }$, which have periodicity with period $i W$.
    In the further limit $W \to \infty$ with constant $\rho$,
    they are degenerated into three infinite-dimensional DPPs.
    One of them is uniform on ${\mathbb{C } }$ and equivalent
    with the Ginibre point process
    studied in random matrix theory, while
    other two systems are isotropic viewed from the origin,
    but non-uniform on ${\mathbb{C } }$.
    We show that the elliptic DPP
    of type $A_N$ is identified with the particle section,
    obtained by subtracting the background effect,
    of the two-dimensional exactly solvable model
    for one-component plasma studied by Forrester.
    Other two exactly solvable models of one-component plasma
    are constructed associated with the elliptic DPPs
    of types $C_N$ and $D_N$.
    Relationship to the Gaussian free field (GFF) on a torus
    is discussed for these three exactly solvable plasma models.
    (For more details, see {\sf arXiv:math-ph/1807.08287}.)

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  • Limit theorems for interacting Brownian motions I, II, III Invited International conference

    Makoto Katori

    Mini Workshop: Modern theory of Particle Systems  ( Faculty of Pure and Applied Mathematics )   2018.6  Faculty of Pure and Applied Mathematics

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    Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

    Dyson model is a stochastic particle system in one dimension R, in which repulsive force acts between any pair of particles with strength proportional to the inverse of distance. This multivariate stochastic process is realized as the system of one-dimensional Brownian motions conditioned never to collide with each other. We can show that this many-body system is exactly solvable and of determinantal in the sense that any spatio-temporal correlation function is expressed by determinant and is controlled by a single continuous function called the correlation kernel. In this lecture, we assume the special initial configuration such that all N particles are concentrated on the origin and we discuss the limit theorems in N ⟶ ∞. Wigner's semicircle law, which is extensively studied in random matrix theory and free probability, is demonstrated as the law of large numbers (LLN), which describes the density profile of particles in R at each time. Two kinds of limits called the bulk scaling limit and the soft-edge scaling limit are introduced in order to obtain determinantal processes with an infinite number of particles. As the central limit theorem (CLT) associated with the latter scaling limit, the Tracy--Widom distribution is discussed.

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  • Bessel Processes, Schramm-Loewner Evolution, and the Dyson Model Invited International conference

    Makoto Katori

    Universite D'Angers, Faculte des Sciences, Department de mathematiques, Colloquium  2018.6 

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  • Macdonald denominators for affine root systems, orthogonal theta functions, and elliptic determinantal processes Invited International conference

    Makoto Katori

    Random Matrices and their Applications  ( kyoto University, Department of Mathematics )   2018.5  kyoto University, Department of Mathematics

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  • Orthogonal theta functions and elliptic determinantal point processes

    Workshop on "Random matrices, determinantal processes and their related topics" in Beppu 2018  2018 

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  • Orthogonal theta functions and elliptic determinantal point processes

    Workshop on "Random matrices, determinantal processes and their related topics" in Beppu 2018  2018 

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  • Hydrodynamic Limits of Multiple SLE Invited International conference

    Makoto Katori

    Tokyo-Seoul Conference in Mathematics - Probability Theory -  2017.12 

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    Language：English   Presentation type：Oral presentation (invited, special)  

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  • Hydrodynamic limit of multipe SLE

    Makoto Katori

    2017.11 

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    Language：Japanese   Presentation type：Oral presentation (general)  

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  • Excursion Processes Associated with Elliptic Combinatorics Invited International conference

    Makoto Katori

    The 16th International Symposium on Stochastic Analysis on Large Scale Interacting Systems  2017.11 

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  • q-拡張から楕円拡張へ Invited

    香取眞理

    第５回 Yokohama Workshop on Quantum Walks  2017.9 

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  • Elliptic Dyson models Invited International conference

    Makoto Katori

    Workshop on Elliptic Hypergeometric Functions in Combinatorics, Integrable Systems and Physics  2017.3 

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  • Conformal invariance of complex Brownian motion and integrable stochastic particle systems

    Half-Day Workshop on Pattern Formation and Statistical Physics with Prof. Helmut R. Brand  2017 

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  • Relaxation Processes in the Non-Equilibrium Dyson Model with an Infinite Number of Particles Invited

    Kick off Meeting for Stochastic Anakysis on Infinite Particle Systems I  2017.1 

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  • Conformal invariance of complex Brownian motion and integrable stochastic particle systems

    Half-Day Workshop on Pattern Formation and Statistical Physics with Prof. Helmut R. Brand  2017 

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  • From q-probability to elliptic-probability

    5th Yokohama Workshop on Quantum Walks  2017 

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  • Hydrodynamic limit of multiple SLE

    2017 

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  • Dyson 模型の非平衡解に見られる緩和過程 Invited

    香取眞理

    ランダム作用素のスペクトルと関連する話題  2016.12 

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  • Martingales and determinantal processes Invited International conference

    Makoto Katori

    The 15th Workshop on Stochastic Analysis on Large Scale Interacging Systems  2016.11 

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  • Complex Nartingales and Determinantal Structures in Nonequilibrium Interacting Particle Systems International conference

    Makoto Katori

    26th IUPAP International Conference on Statistical Physics (StatPhys26)  2016.7 

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  • Complex martingales and determinantal processes Invited International conference

    Makoto Katori

    New approaches to non-equilibrium and random systems: KPZ integrability, universality, applications and experiments  2016.3 

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  • Complex martingales and determinantal structures in nonequilibrium interacting particle systems

    千葉大確率論研究会  2016 

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  • Determinantal interacting particle systems Invited International conference

    Makoto Katori

    International Symposium `RIKKYO MathPhys 2016'  2016.1 

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  • Complex martingales and determinantal structures in nonequilibrium interacting particle systems

    Chiba University Probability Theory Workshop  2016 

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  • Complex Martingales and Determinantal Structures in Nonequilibrium Interacting Particle Systems

    26th IUPAP International Conference on Statistical Physics (StatPhys26)  2016 

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  • Relaxation processes in the non-equilibrium Dyson model with an infinite number of particles

    Spectra of Randomn Operators and Related Topics  2016 

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  • Noncolliding pinned Brownian motions Invited International conference

    Makoto Katori

    Spectra of Random Operators and Related Topics  2015.12 

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  • ダイナミカルなランダム行列と棲み分けの問題 Invited

    香取眞理

    生命ダイナミクスの数理とその応用：理論からのさらなる深化  2015.12 

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    Language：Japanese   Presentation type：Oral presentation (invited, special)  

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  • Bessel Process, Schramm-Loewner Evolution, and the Dyson Model Invited International conference

    Makoto Katori

    RMT2015: Random matrix theory from fundamental mathematics to biological applicatoins  2015.11 

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  • Elliptic Bessel Process and Elliptic Dyson Model Realized as Temporally Inhomogeneous Processes Invited International conference

    Makoto Katori

    14th Stochastic Analysis on Large Scale Interacting Systems  2015.10 

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  • 可換砂山模型の数理 Invited

    香取眞理

    日本物理学会2015年秋季大会  2015.9 

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  • Abelian sandpile models in statistical mechanics Invited International conference

    Makoto Katori

    Workshop on `Probabilistic models with determinantal structure'  2015.4 

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  • Noncolliding Brownian bridges associated with elliptic functions

    関西確率論セミナー  2015 

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  • Determinantal martingales and determinantal processes

    立教大学数理物理学研究センター 2015年度第3回定例セミナー  2015 

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  • Elliptic determinantal evaluations and diffusion processes Invited International conference

    Makoto Katori

    Spectra of Random Operators and Related Topics  2015.1 

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  • Noncolliding Brownian bridges associated with elliptic functions

    2015 

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  • Determinantal martingales and determinantal processes

    Seminar at Research Center for Mathematical Physics, Rikkyo University  2015 

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  • Martingales for determinantal log-gases Invited International conference

    Makoto Katori

    YITP workshop `Interface fluctuations and KPZ universality class - unifying mathematical, theoretical, and experimental approaches'  2014.12 

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  • Elliptic determinantal processes Invited International conference

    Makoto Katori

    The 13th Workshop on Stochastic Analysis on Large Scale Interacting Systems  2014.11 

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  • Determinantal martingales and determinantal processes International conference

    Makoto Katori

    International Conference on Stochastic Processes, Analysis and Mathematical Physics  2014.8 

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  • 行列式過程としてダイソン模型をどれだけ拡張できるか

    研究集会「無限粒子系と確率場の諸問題IX」  2014 

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  • 時間発展するランダム行列

    第２１回沼津研究会  2014 

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  • 時間発展するランダム行列固有値模型の揺動と相関

    2014年度夏学期第10回駒場物性セミナー  2014 

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  • Extensions of Dyson's model keeping determinantal solvability

    2014 

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  • Complex Brownian motion representation and Eynard-Mehta-type correlation kernel

    Workshop on ``Determinantal Processes and Related Topics"  2013 

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  • Complex Brownian motion representation of the Dyson model

    関西確率論セミナー 拡大セミナー  2013 

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  • Conformal martingale representations of log-gases [PP2-3-17 Poster]

    25th IUPAP International Conference on Statistical Physics (STATPHYS25)  2013 

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  • Determinantal martingales and determinantal processes

    Workshop `Random analytic functions, random matrices, and determinantal processes'  2013 

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  • Determinantal martingales and correlations of noncolliding random walks

    12th workshop on Stochastic Analysis on Large Scale Interacting Systems  2013 

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  • An elliptic extension of Dyson's Brownian motion model

    Workshop `New Topics on Stochastic and Quantum Interacting Particle Systems'  2013 

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  • Determinantal martingales and noncolliding diffusion processes

    Workshop `Spectra of Random Operators and Related Topics'  2013 

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  • Complex Brownian motion representation and Eynard-Mehta-type correlation kernel

    Workshop on ``Determinantal Processes and Related Topics"  2013 

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  • Complex Brownian motion representation of the Dyson model

    Kansai Probability Seminar (Kyoto Seminar) Extended  2013 

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  • Conformal martingale representations of log-gases

    25th IUPAP International Conference on Statistical Physics (STATPHYS25)  2013 

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  • Determinantal martingales and determinantal processes

    Workshop `Random analytic functions, random matrices, and determinantal processes'  2013 

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  • Determinantal martingales and correlations of noncolliding random walks

    12th workshop on Stochastic Analysis on Large Scale Interacting Systems  2013 

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  • An elliptic extension of Dyson's Brownian motion model

    Workshop `New Topics on Stochastic and Quantum Interacting Particle Systems'  2013 

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  • Determinantal martingales and noncolliding diffusion processes

    Workshop `Spectra of Random Operators and Related Topics'  2013 

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  • Vicious Brownian motion, O'Connell's process, and equilibrium Toda lattice Invited International conference

    Makoto Katori

    EPSRC Symposium Workshop on Interacting particle systems, growth models, and random matrices  2012.3 

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  • 条件付ブラウン運動・ＳＬＥ・ランダム行列・量子戸田格子

    横浜国立大工学部 玉野セミナー  2012 

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  • 条件付ブラウン運動・SLE・ランダム行列・量子戸田格子

    行列模型とその周辺  2012 

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  • Vicious Brownian motion, O'Connell process, and equilibrium Toda lattice

    Workshop on Recent Topics of Statistical Mechanics and Probability Theory  2012 

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  • System of complex Brownian motions associated with the O'Connell process

    研究集会「無限粒子系、確率場の諸問題 VIII」  2012 

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  • Determinantal formula appearing in non-determinantal process

    Spectra of Random Operators and Related Topics  2012 

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  • Vicious Brownian motions, entire functions, and quantum Toda lattice

    Novel Development of Statistical Physics  2012 

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  • Vicious Brownian motion, O'Connell process, and equilibrium Toda lattice

    Workshop on Recent Topics of Statistical Mechanics and Probability Theory  2012 

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  • System of complex Brownian motions associated with the O'Connell process

    2012 

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  • Determinantal formula appearing in non-determinantal process

    Spectra of Random Operators and Related Topics  2012 

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  • Vicious Brownian motions, entire functions, and quantum Toda lattice

    Novel Development of Statistical Physics  2012 

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  • On Matsumoto-Yor process and O'Connell process

    研究集会「無限粒子系、確率場の諸問題 VII」  2011 

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  • Vicious Brownian motion with Toda lattice potential and O'Connell's process

    ランダム作用素のスペクトルと関連する話題  2011 

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  • On Matsumoto-Yor process and O'Connell process

    2011 

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  • Vicious Brownian motion with Toda lattice potential and O'Connell's process

    2011 

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  • Determinantal Processes and Entire Functions International conference

    Makoto Katori

    34th Conference on Stochastic Processes and Their Applications  2010.9 

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  • 「統計力学模型とSLE」「SLEに関する話題」

    勉強会「Loewner 方程式とSLE」  2010 

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  • Stochastic Loewner Evolutions and Statistical Mechanics

    第 53 回函数論シンポジウム  2010 

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  • 非衝突ブラウン運動・ランダム行列・整関数

    第９回岡シンポジウム  2010 

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  • Dyson 模型の複素ブラウン運動表示と行列式型相関関数

    大岡山談話会  2010 

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  • Stochastic Loewner Evolutions and Statistical Mechanics

    2010 

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  • Entire functions and relaxation processes of infinite particle systems Invited International conference

    Makoto Katori

    Conference on Probability and Stochastic Processes  2009.11 

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  • Zeros of Airy Function and Relaxation Process Invited International conference

    Makoto Katori

    International Conference `Selfsimilar Processes and their Applications'  2009.7 

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  • 連続関数空間上の共形不変な確率測度とSchramm-Loewner Evolution Invited

    香取眞理

    日本数学会2009年度年会  2009.3 

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  • Non-Equilibrium Dynamics of Dyson's Model with Infinite Particles

    古典および量子ダイナミクス・非平衡統計力学に関するワークショップ  2009 

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  • SLE/CFT correspondence

    Workshop on "SLE and related topics"  2009 

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  • ディラック方程式・量子ウォーク・グラフェン

    量子ウォークの相対論的記述と固有値解析  2009 

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  • 臨界現象・フラクタル曲線とSchramm-Loewner Evolution

    Summer School 数理物理 2009  2009 

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  • 数理物理学の新展開--ランダム行列とSLE

    第54回物性若手夏の学校  2009 

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  • Zeros of entire functions and relaxation processes

    VIIIth Symposium quot;Stochastic Analysis on Large Scale Interacting Systems"  2009 

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  • Dyson's Brownian motion model with beta=2 and entire functions

    ランダム作用素のスペクトラルと関連する話題  2009 

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  • SLE/CFT correspondence

    Workshop on "SLE and related topics"  2009 

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  • Zeros of entire functions and relaxation processes

    VIIIth Symposium "Stochastic Analysis on Large Scale Interacting Systems"  2009 

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  • Dyson's Brownian motion model with beta=2 and entire functions

    2009 

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  • Multiple orthogonal polynomials and noncolliding diffusion processes Invited

    Makoto Katori

    2008.11 

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  • Multiple orthogonal polynomials and noncolliding Brownian motions Invited International conference

    Makoto Katori

    Workshop on Stochastic Analysis on Large Scale Interacting Systems  2008.11 

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  • 確率微分方程式と相転移・臨界現象 Invited

    香取眞理

    第１３回久保記念シンポジウム,井上科学振興財団  2008.10 

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  • 非衝突ブラウン運動・多重エルミート関数・ランダム行列 Invited

    香取眞理

    九州大学大学院理学研究院物理部門談話会,九州大学大学院理学府  2008.7 

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  • Noncolliding Brownian motions with arbitrary initial configuration and multiple Hermite polynomials Invited International conference

    Makoto Katori

    Workshop on Combinatorics and Statistical Physics/Erwin Schrodinger International Institute for Mathematical Physics (ESI)  2008.5 

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  • Maximum height distribution of noncolliding Bessel bridges Invited International conference

    Makoto Katori

    ESI Programme on Combinatorics and Statistical Physics/Erwin Schrodinger International Institute for Mathematical Physics (ESI)  2008.3 

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  • Multiple orthogonal polynomials and determinantal processes Invited International conference

    Makoto Katori

    Workshop on Random matrices, special functions and related topics/Research Institute for Mathematical Science (RIMS), Kyoto University  2008 

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  • An Introduction to Schramm-Loewner Evolution

    研究集会「統計物理に関連する数学的話題」,東工大理工学研究科数学教室  2007 

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  • Schramm-Loewner Evolution (SLE) and Conformal Restriction

    保型形式・無限可積分系合同合宿(2007),東京大学大学院数理科学研究科  2007 

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  • ブラウン運動・SLE・２次元臨界現象(Lawler, Schramm, Werner らの結果の紹介)

    非可換解析とミクロ・マクロ双対性,京都大学数理解析研究所  2007 

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  • Noncolliding diffusion processes and determinantal processes

    ランダム作用素のスペクトルと関連する話題,京都大学大学院人間・環境学研究科  2007 

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  • ブラウン運動とリーマンのゼータ関数

    立教大学理論物理学研究室セミナー  2007 

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  • Noncolliding diffusion processes and determinantal processes

    2007 

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  • 量子ウォークの特異な拡散現象

    九州大学大学院工学研究院特別講義,九州大学大学院工学研究院エネルギー量子工学部門  2006 

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  • Wigner formula of rotation matrices and quantum walks

    研究集会「非線型波動現象における基礎理論,数値計算および実験のクロスオーバー」,九州大学応用力学研究所  2006 

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  • 量子ウォークの特異な極限分布

    立教大学理論物理学研究室セミナー  2006 

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  • 時間的に非斉次な非衝突ブラウン運動

    東京無限可積分セミナー,東京大学数理科学研究科  2005 

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  • ワイル粒子の軌道状態と量子ウォークの極限分布

    日本物理学会 2005 年度秋季大会,同志社大学,日本物理学会  2005 

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  • 量子ウォークとワイル方程式

    日本物理学会 2005 年度秋季大会,同志社大学,日本物理学会  2005 

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  • 非衝突ブラウン運動と Tracy-Widom 分布

    研究集会「無限粒子系、確率場の諸問題」,奈良女子大学理学部  2005 

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  • 非衝突拡散粒子系とランダム行列理論

    日本物理学会第59回年次大会(九大),日本物理学会  2004 

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  • Vicious Walks and Random Matrices

    Satellite Meeting of STATPHYS 22 in Seoul, Korea,Nonequilibrium Statistical Physics of Complex Systems/Korea Institute for Advanced Study (KIAS),IUPAP  2004 

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  • 非衝突拡散過程と四元数行列式

    可積分系数理の展望と応用,京都大学数理解析研究所  2004 

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  • Vicious Walks, Schur Functions, and Random Matrix Theory

    Joint Seminar in Probability (Chinese Academy of Science, Peking Univ., Beijing Normal Univ., China)/Inst. Applied Math., Chinese Academy of Science, China  2004 

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  • Matrix-valued Stochastic Processes and Noncolliding Diffusion Particle Systems

    Workshop on Infinite Particle Systems and Critical Phenomena/Beijing Jiaotong University  2004 

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  • Nonintersecting paths, noncolliding diffusion processes and representation theory

    表現論における組み合わせ論的手法とその応用/京都大学数理解析研究所  2004 

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  • 時間的に非斉次な非衝突ブラウン運動

    立教SFR研究会「弦理論と重力理論の数学的構造解明に関する学際的研究」,立教大学学術推進特別重点資金(SFR)自由プロジェクト研究  2004 

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  • Vicious Walks and Random Matrices

    Satellite Meeting of STATPHYS 22 in Seoul, Korea,Nonequilibrium Statistical Physics of Complex Systems/Korea Institute for Advanced Study (KIAS),IUPAP  2004 

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  • Vicious Walks, Schur Functions, and Random Matrix Theory

    Joint Seminar in Probability (Chinese Academy of Science, Peking Univ., Beijing Normal Univ., China)/Inst. Applied Math., Chinese Academy of Science, China  2004 

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  • Matrix-valued Stochastic Processes and Noncolliding Diffusion Particle Systems

    Workshop on Infinite Particle Systems and Critical Phenomena/Beijing Jiaotong University  2004 

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  • Nonintersecting paths, noncolliding diffusion processes and representation theory

    Combinatorical Methods in Representation Theory/RIMS, Kyoto University  2004 

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  • 無限粒子 vicious walk とエアリー過程

    日本物理学会  2003 

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  • Noncolliding systems of diffusion particles and multi-matrix models

    大規模相互作用系の確率解析(日本数学会シンポジウム)  2003 

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  • Noncolliding Brownian particles, Schur polynomials, and GUE/GOE two-matrix model

    京都大学基礎物理学研究所セミナー,京都大学基礎物理学研究所  2003 

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  • 非衝突ランダムウォーク, シューア関数, 多層行列模型

    非線形波動および非線形力学系の数理とその応用(九大応用力学研究所研究集会；研究集会報告 2004年4月),九州大学応用力学研究所  2003 

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  • 非衝突拡散粒子系とランダム行列理論

    確率モデルの統計力学(京大基研研究集会),京都大学基礎物理学研究所  2003 

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  • Noncolliding Brownian particles, Schur polynomials, and GUE/GOE two-matrix model

    2003 

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  • 繰り込み群による vicious walk の研究

    日本物理学会  2002 

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  • vicious walks の連続極限とランダム行列

    日本物理学会  2002 

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  • Scaling limit of vicious walkers, Schur functions and Gaussian random matrix ensembles

    Oxford University, UK  2001 

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  • Scaling limit of vicious walkers, Schur functions and Gaussian random matrix ensembles

    Oxford University, UK  2001 

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  • SOC as a critical phenomena in a nonconservative Abelian sandpile model

    ICTP,Trieste,Italy  2000 

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  • SOC as a critical phenomena in a nonconservative Abelian sandpile model

    ICTP,Trieste,Italy  2000 

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  • 粒子消滅を伴う可換砂山モデルの非臨界性

    日本物理学会第54回年会,広島大学,日本物理学会  1999 

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  • 3次元Directed Percolationの臨界挙動

    日本物理学会第54回年会,広島大学,日本物理学会  1999 

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  • バッタの相変異における協同現象

    日本物理学会第54回年会,広島大学,日本物理学会  1999 

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  • Chiral Potts Models, Friendly Walkers and Directed Percolation Problem;「Markov 連鎖とその統計力学への応用」

    平成9年度科研費基盤研究（A）「確率論の総合的研究」研究会,神戸大（招待講演）  1998 

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  • 非等方的な可換砂山モデルの厳密解

    日本物理学会第53回年会,東邦大学,日本大学  1998 

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  • Forest dynamics with canopy gap expansion and stochastic Ising model

    STATPHYS 20, Paris, France/IUPAP  1998 

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  • Effect of anisotropy on the self-organized critical states of Abelian sandpile models

    International Conference on Percolation and Disordered Systems,Giessen, Germany/International Conference on Percolation and Disordered Systems,Giessen,Germany.  1998 

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  • Chiral Potts models, friendly walkers and directed percolation problem

    STATPHYS 20, Paris, France IUPAP  1998 

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  • A stochastic lattice model for locust outbreak

    International Conference on Percolation and Disorderd Systems, Giessen, Germany/International Conference on Percolation and Disordered Systems,Giessen,Germany.  1998 

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  • 砂山モデルにおけるなだれサイズ分布の多様性

    日本物理学会秋の分科会,琉球大学,沖縄国際大学,日本物理学会  1998 

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  • 非等方的な可換砂山モデルの厳密解Ⅱ

    日本物理学会秋の分科会,琉球大学,沖縄国際大学,日本物理学会  1998 

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  • 森林の林冠ギャップの空間分布とイジング模型Ⅱ

    日本物理学会秋の分科会,琉球大学,沖縄国際大学,日本物理学  1998 

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  • Forest dynamics with canopy gap expansion and stochastic Ising model

    STATPHYS 20, Paris, France/IUPAP  1998 

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  • Effect of anisotropy on the self-organized critical states of Abelian sandpile models

    International Conference on Percolation and Disordered Systems,Giessen, Germany/International Conference on Percolation and Disordered Systems,Giessen,Germany.  1998 

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  • Chiral Potts models, friendly walkers and directed percolation problem

    STATPHYS 20, Paris, France IUPAP  1998 

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  • A stochastic lattice model for locust outbreak

    International Conference on Percolation and Disorderd Systems, Giessen, Germany/International Conference on Percolation and Disordered Systems,Giessen,Germany.  1998 

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  • クラスター変分近似の収束性とコヒーレント異常

    クラスター変分法に関するミニシンポジウム,東工大（招待講演）  1997 

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  • Chiral Potts模型とDirected Percolation ＩＩ

    日本物理学会年会,名城大  1997 

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  • Chiral Potts模型とDirected Percolation I

    日本物理学会講演概要集、日本物理学会年会,名城大  1997 

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  • 相互作用する randem walks の数え上げと Chiral Potts 模型

    日本物理学会秋の分科会,神戸大  1997 

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  • 森林の林冠ギャップの空間分布とイジング模型

    日本物理学会講演概要集、日本物理学会秋の分科会,神戸大  1997 

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  • 一般化した砂山モデルについて

    日本物理学会秋の分科会,神戸大  1997 

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  • Cluster Variational Approach to Non-equilibrium Lattice Models Invited

    M.Katori

    Theory and Applications of the Cluster Variation and Path Probability Methods ed J.L.Moran-Lopez and J.M.Sanchez  1996.4 

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    Language：English   Presentation type：Oral presentation (general)  

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  • Directed Percolationの展開係数における規則性II

    日本物理学会（第51回年会）講演概要集,日本物理学会  1996 

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  • 非対称Directed Percolationの級数展開

    日本物理学会秋の分科会,山口大  1996 

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  • 新しい砂山モデルに対する平均場近似とモンテカルロシミュレーション

    日本物理学会秋の分科会,山口大  1996 

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  • Directed Percolationの級数展開係数のballot数表示

    日本物理学会講演概要集、日本物理学会秋の分科会,山口大  1996 

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  • 自己組織化臨界現象を示す幾つかのモデル

    「パーコレーション,無限粒子系の数理」（平成8年度科学研究費補助金 基盤研究A（1））「確率論の総合的研究」,横浜国立大（招待講演）  1996 

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  • Catalan numbers in the percolation probability series for the directed square lattice

    「パーコレーション,無限粒子系の数理」（平成8年度科学研究費補助金 基盤研究A（1））「確率論の総合的研究」,横浜国立大（招待講演）  1996 

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  • Catalan numbers in the percolation probability series for the directed square lattice

    1996 

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  • 無限粒子系の非可逆な確率過程の研究

    中央大学理工学研究所年報,中央大学理工学研究所  1995 

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  • 非平衡格子モデルにおけるDualityとUniversality

    日本物理学会（第50回年会）講演概要集,日本物理学会  1995 

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  • Contact Process, Directed Percolation and Beyond

    Meeting on Pattern Formation (KEK),高エネルギー研究所  1995 

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  • Cluster variational Approach to Non-equilibrium Lattice Models

    International Workshop on the Theory and Applications of the Cluster Variation and Path Probability Methods, (Mexico) Proceedings/Plenum Press  1995 

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  • Time-Reversal Duality and Planar Lattice Duality in Non-equilibrium Lattice Models

    International Conference on Future of Fractals(Aichi),/World Scientific Pub. Co.  1995 

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  • クラスター近似による砂山モデルの高さ分布の計算

    日本物理学会（1995年秋の分科会）講演概要集,日本物理学会  1995 

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  • 確率的セルラ・オートマンのedgeプロセスとその裏格子プロセス

    Fractals日本物理学会（1995年秋の分科会）講演概要集,日本物理学会  1995 

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  • Stochastic Cellular Automataに関する最近の話題

    平成7年度科研費報告書「確率論の総合的研究」,平成7年度科研費基盤研究A(1)  1995 

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  • Contact Process, Directed Percolation and Beyond

    Meeting on Pattern Formation (KEK)  1995 

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  • Cluster variational Approach to Non-equilibrium Lattice Models

    International Workshop on the Theory and Applications of the Cluster Variation and Path Probability Methods, (Mexico) Proceedings/Plenum Press  1995 

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  • Time-Reversal Duality and Planar Lattice Duality in Non-equilibrium Lattice Models

    International Conference on Future of Fractals(Aichi),/World Scientific Pub. Co.  1995 

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  • Introduction to Non-equilibrium Lattice Models

    東北大学金属材料研究所セミナー  1994 

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  • 高次元における拡散を伴ったコンタクト・プロセスの相図

    日本物理学会（第49回年会）講演概要集,日本物理学会  1994 

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  • The Holley-Liggett argument revisited : an application to the generalized contact process

    ICM94 Abstracts/International Mathematical Union  1994 

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  • 1次元非対称exclusion processの定常分布について

    日本物理学会（1994年秋の分科会）講演概要集,日本物理学会  1994 

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  • Introduction to Non-equilibrium Lattice Models

    1994 

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  • The Holley-Liggett argument revisited : an application to the generalized contact process

    ICM94 Abstracts/International Mathematical Union  1994 

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  • Phase transition in contact process and its related processes

    確率論セミナー主催シンポジウム講演概要集,確率論セミナー  1993 

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  • 粒子系における非可逆な定常状態について

    数理解析研講究録,京大数理解析研究所  1993 

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  • 拡張された1次元コンタクト・プロセスの臨界値に対する評価II

    日本物理学会（1993年秋の分科会）講演概要集,日本物理学会  1993 

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  • 1次元Pain Annihilation Model における相転移の存在証明

    日本物理学会（1993年秋の分科会）講演概要集,日本物理学会  1993 

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  • 伝染のモデルと交通渋滞のモデル

    東北大学理学部物理セミナー  1993 

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  • コンタクト・プロセスの相転移現象

    東北大学工学部数物談話会  1993 

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  • Phase transition in contact process and its related processes

    1993 

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  • 触媒表面の数理モデル

    物性研究,物性研究刊行会  1992 

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  • 無限粒子系の物理と数学

    物性研究,物性研究刊行会  1992 

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  • 拡張された1次元コンタクト・プロセスの臨界値に対する評価

    日本物理学会講演概要集,日本物理学会  1992 

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  • 拡散を伴うコンタクト・プロセスの相図について

    物性研だより,東京大学物性研究所  1992 

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  • 拡散を伴ったコンタクト・プロセスについて

    物性研究,物性研究刊行会  1992 

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  • 非可逆な化学反応モデルにおける拡散の効果について

    物性研究,物性研究刊行会  1991 

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  • コンタクト・プロセスにおける感染領域の定常分布について

    物性研究,物性研究刊行会  1990 

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  • Contact Processの定常状態における相転移現象について

    統計数理,統計数理研究所  1990 

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  • Window-CID-CAMによるContact Processの研究

    物性研究,物性研究刊行会  1989 

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  • カノニカル・シリーズの作り方-クラスター平均場近似と相関等式切断近似-

    物性研究,物性研究刊行会  1989 

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  • 相転移とCAM理論

    物性研究,物性研究刊行会  1988 

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  • GT線における非線形帯磁率について

    物性研究,物性研究刊行会  1986 

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  • レプリカ理論と非線形帯磁率

    物性研究,物性研究刊行会  1985 

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Awards

  • 中央大学学術研究奨励賞

    2022.2   Chuo University  

    Makoto Katori

  • The MSJ Analysis Prize

    2021.9   The Mathematical Society of Japan   Interacting particle systems related to statistical mechanics

    Makoto Katori

  • Editor's Pick

    2020.8   American Institute of Physics   Conformal welding problem, flow line problem, and multiple Schramm-Loewner evolution

    Makoto Katori, Shinji Koshida

  • JPSJ Papers of Editors' Choice

    2015.10   Journal of the Physical Society of Japan, The Physical Society of Japan   Self-Elongation with Sequential Folding of a Filament of Bacterial Cells

    Ryojiro Honda, Jun-ichi Wakita, Makoto Katori

  • 第５回 井上科学研究奨励賞

    1989  

  • 5th Inoue Research Award for Young Scientists

    1989  

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Research Projects

  • General Theory of Higher Dimensional Stochastic Dynamics and its Applications to Non-Equilibrium Complex Systems

    Grant number：24K06888  2024.4 - 2029.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)  Chuo University

    Makoto Katori

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    Authorship：Principal investigator  Grant type：Competitive

    Grant amount： \4810000 （ Direct Cost: \3700000 、 Indirect Cost： \1110000 ）

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  • Universality of determinantal point processes and analysis of random phenomena

    Grant number：23K25774  2023.4 - 2028.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)  Kyushu University

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    Authorship：Coinvestigator(s)  Grant type：Competitive

    Grant amount： \18460000 （ Direct Cost: \14200000 、 Indirect Cost： \4260000 ）

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  • Development, evolution, and new development of stochastic analysis of infinite particle systems

    Grant number：21H04432  2021.4 - 2026.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (A) 

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    Grant amount： \41340000 （ Direct Cost: \31800000 、 Indirect Cost： \9540000 ）

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  • フェルミオン点過程と共形不変SLE曲線による確率場の総合的理論の構築

    2019.4 - 2024.3

    日本学術振興会  科学研究費補助金、基盤研究（C) 

    香取 眞理

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    Authorship：Principal investigator  Grant type：Competitive

    Grant amount： \4290000 （ Direct Cost: \3300000 、 Indirect Cost： \990000 ）

    ランダム行列理論は１次元線上や２次元平面上のランダムな点集合であるフェルミオン点過程の確率理論を与え，平面上の臨界統計力学模型とフラクタル模型のスケーリング連続極限を表現するシュラム・レヴナー発展(SLE)は共形変換不変な確率測度をもつランダムな曲線の時間発展理論である。本研究ではこれら点や曲線に対する確率理論の研究を深め，それらで特徴づけられる確率場に対して総合的な新理論を構築する。具体的には，高次元リーマン多様体上のフェルミオン点過程の一般論を展開し，１成分あるいは２成分プラズマ模型を経由して自由ガウス場，さらにそのリウビル量子重力場への変換を明らかにする。局所的な場の接続を分類し，多重SLEでコントロールする。多重SLEの普遍的な確率法則の導出やDLA(拡散律速凝集)模型のフラクタル次元決定など，多くの未解決問題に挑戦する。

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  • Stochastic Analysis of Random Phenomena from the Viewpoint of Determinantal Point Processes

    2018.4 - 2022.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research 

    Shirai, Tomoyuki

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    Grant type：Competitive

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  • Stochastic Analysis for Infinite Particle Systems

    2016.4 - 2021.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research 

    Osada, Hirofumi

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    Grant type：Competitive

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  • New Theory of Fluctuations and Correlations in Exactly Solvable Models of Nonequilibrium Statistical Mechanics

    2014.4 - 2019.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research, Kiban (C) 

    Katori, Makoto

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    Authorship：Principal investigator  Grant type：Competitive

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  • Collective motion of bacterial cells in a two-dimensional circular pool

    Grant number：15K13537  2015.4 - 2018.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Challenging Exploratory Research  Chuo University

    Wakita Jun-ichi, KATORI Makoto, MATSUSHITA Mitsugu, YAMAMOTO Ken, NARIZUKA Takuma, HONDA Ryojiro, TSUKAMOTO Shota, HARADA Shohei, UMEDA Sora, NISHIOKA Mizuho

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    Grant amount： \2730000 （ Direct Cost: \2100000 、 Indirect Cost： \630000 ）

    Recently, various types of collective behavior observed in swarming micro-organisms, marching insects, flocking birds, and walking pedestrians have been studied in the field of physics. The relation between individual behavior and collective behavior has been investigated from the view point of statistical physics. In our studies, we found that Bacillus subtilis cells as a kind of micro-organisms showed six types of collective behavior depending on the reduced cell length (defined as the ratio of cell length to pool diameter) and the cell density in a circular pool which was made on an agar plate surface. Then, we have confirmed that the interaction of a cell with the brim of a pool, the interaction between cells, and the fluctuation in the moving direction of cells are essential to the collective behavior.

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  • Study of Determinantal Point Processes and their Generalizations

    2014.4 - 2018.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research 

    Shirai, Tomoyuki

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    Grant type：Competitive

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  • 無限粒子系とランダム行列の確率解析

    Grant number：16H02149  2016.4 - 2017.3

    日本学術振興会  科学研究費助成事業  基盤研究(A)  九州大学

    長田 博文, 種村 秀紀, 白井 朋之, 香取 眞理, 熊谷 隆, 舟木 直久

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    Grant amount： \42640000 （ Direct Cost: \32800000 、 Indirect Cost： \9840000 ）

    干渉ブラウン運動のtagged粒子の不変原理に関して、従来より適切かつ精密な定式化を行い、Kipnis-Varadhanの不変原理の対応物が成立することを証明した。
    従来は、Palm測度に対して、無限個の環境粒子系にたいして、tagged粒子のブラウン運動への収束が「測度収束」の意味で成立するという形で、主張が定式化されてきた。これは、80年代前半に行われたGuo-Papanicolauの研究以来の伝統的な定式化ではあるが、tagged粒子から見た他の無限個の粒子家の挙動を記述する確率微分方程式に対する解析となるため、すぐには元来の問題との関係が分かりにくい。
    それに対して、今回は、粒子のラベルを考慮し構造に入れることにより、元々の平行移動不変な平衡分布に関して、可逆な確率力学を記述する確率微分方程式を考え、その個々の粒子が、ブラウン運動に初期条件に関して測度収束するという、より自然なわかりやすい定式化となった。
    また、応用として、1次元の無限粒子系が互いに衝突しない（順序を入れ替えない）という性質をもつとき、極限が常に退化するという結果を得た。この事実自体は、当然の結果だが、ポイントはこれが常に成立するということを、幾何的な結果から平易に示したという一般性を備えている点である。
    ランダム行列に関係する干渉ブラウン運動は、対数関数（2次元クーロンポテンシャル）で相互作用する確率力学である。また、干渉ブラウン運動を含む広い範囲の無限次元確率微分方程式に対して一般論を構築し、更に発展させている最中だが、これに関する最近の研究結果をまとめてreview論文として報告した。

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  • Developing micro-macro-structure connection engineering for novel functions of Si-LED based on dressed photons

    Grant number：15K13374  2015.4 - 2016.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Challenging Exploratory Research  The University of Tokyo

    OHTSU Motoichi, KATORI Makoto, NARUSE Makoto

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    Grant amount： \3770000 （ Direct Cost: \2900000 、 Indirect Cost： \870000 ）

    Highly efficient and high power Si-LEDs were fabricated by dressed-photon-phonon (DPP)-assisted annealing. It was found that Boron atoms, a DPP-creation source, formed a pair, and the separation between the two atoms in the pair was three-times the lattice constant of the Si crystal. The atom pair aligned along the plane normal to the direction of the incident light beam used for the annealing. It was also normal to the polarization direction of this light. Simultaneously with these experimental works, novel mathematical scientific model was developed to analyze the light-matter interaction in a mesoscopic space. The results of the analyses agreed well with the experimental results. Furthermore, statistical model of energy transfer in a random medium via dressed photons was developed.

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  • Stochastic geometry and dynamics of infinite particle systems interacting with two-dimensional Coulomb potential

    Grant number：24244010  2012.4 - 2016.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (A)  Kyushu University

    Osada Hirofumi, KOTANI Shinichi, KATORI Makoto, SHINPDA Masato, OTOBE Yoshiki

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    Grant amount： \28470000 （ Direct Cost: \21900000 、 Indirect Cost： \6570000 ）

    We establish a general theory for solving infinite-dimensional stochastic differential equations (ISDE) with symmetry typically appearing in statistical mechanics. In particular, we prove the pathwise uniqueness and the existence of the strong solution under a very general framework. This method is novel, and regards the tail sigma field of the configuration space as a boundary of the ISDE. Furthermore, if the tail sigma field is trivial, then a strong solution exists. If the set of probability-one events is unique, then the pathwise uniqueness of solution holds.
    The method is effective for the ISDE with logarithmic interaction potentials, which appear in random matrix theory.

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  • Stochastic analysis of infinite particle systems in nonequilibruim

    Grant number：23540122  2011.4 - 2015.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)  Chiba University

    TANEMURA Hideki, KATORI Makoto, SASAMOTO Tomohiro

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    Grant amount： \4810000 （ Direct Cost: \3700000 、 Indirect Cost： \1110000 ）

    We study existence and uniqueness of infinite dimensional stochastic differential equations (ISDEs). We clarified the relation between the uniqueness of solutions and the triviality of tail sigma fields. Applying the result, we obtained the uniqueness of strong solutions of ISDEs describing the systems of Brownian motions with long range interaction including logarithmic potential, and determined the Dirichlet forms associated with the systems.

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  • Study on stochastic processes with determinantal structure

    Grant number：22340020  2010.4 - 2014.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)  Kyushu University

    SHIRAI Tomoyuki, TANEMURA Hideki, KATORI Makoto, OSADA Hirofumi

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    Grant amount： \13780000 （ Direct Cost: \10600000 、 Indirect Cost： \3180000 ）

    Correlation functions of the eigenvalues of certain random matrices can be expressed by using determinant. A point configuration whose correlation functions are determinants has repulsive property and is called a determinantal point process. Many mathematical objects can be described as a determinantal point process and analyzed precisely. We study the Ginibre point process, which is a typical model of determinantal point process, and we use this determinantal point process instead of poisson point process as a model of base stations of a cellular network and analyze it. We investigated determinantal point processes from both theoretical and applied mathematical points of view.

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  • Statistical Mechanics for Random Curves and Patterns with Applications

    2009.4 - 2014.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research, Kiban (C) 

    Katori, Makoto

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    Authorship：Principal investigator  Grant type：Competitive

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  • Infinite-dimensional stochastic dynamical systems motivated by random matrices and statistical physics

    Grant number：21340031  2009 - 2011

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)  Kyushu University

    OSADA Hirofumi, FUNAKI Tadahisa, TANEMURA Hideki, SHIRAI Tomoyuki, KATORI Makoto, OTOBE Yoshiki, SHINODA Masato, YANO Yuko, YANO Kouji

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    Grant amount： \16640000 （ Direct Cost: \12800000 、 Indirect Cost： \3840000 ）

    We have established a general construction theorem and an SDE representation theorem for interacting Brownian motions with 2D Coulomb potentials. We have applied them to the representative random point fields arising from Random Matrix Theory such as Ginibre, Dyson, Bessel random point fields, and have detected and solve the infinite-dimensional stochastic differential equations describing the associated stochastic dynamics. We prove the Palm measures of Ginibre random point field have very strange property that is very different from usual Gibbs measures with Ruelle' s class interaction potentials. We have constructed the time evolutional model of 2D Young diagram and have proved its scaling limit.

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  • Particle systems with interaction

    Grant number：19540114  2007 - 2010

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)  Chiba University

    TANEMURA Hideki, KONNO Norio, KATORI Makoto, SASAMOTO Tomohiro

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    Grant amount： \4420000 （ Direct Cost: \3400000 、 Indirect Cost： \1020000 ）

    A stochastic process is called determinantal if its correlation functions are represented by determinants. During the research we proved that for any fixed configuration the noncolliding Brownian motion and the noncolliding squared Bessel process are determinantal. When number of particle is infinite, we gave sufficient conditions so that the noncolliding processes are exist and have continuous paths. We also showed the relaxation phenomena for the processes.

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  • Random Matrix Theory for Condensed Matters

    2005.4 - 2009.3

    Japan Society for the Promotion of Science  Gtants-in-Aid for Scientific Research 

    Katori, Makoto

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    Authorship：Principal investigator  Grant type：Competitive

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  • Formation Mechanism of Growing Random Patterns

    Grant number：18340115  2006 - 2009

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)  Chuo University

    MATSUSHITA Mitsugu, KATORI Makoto, TAGUCHI Yoshihiro, MATSUYAMA Touhei, SUDA Junichiro, YAMAZAKI Yoshihiro

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    Grant amount： \11790000 （ Direct Cost: \10500000 、 Indirect Cost： \1290000 ）

    We have mainly studied three topics on universal structural and statistical properties of random patterns seen in nature and our society. 1. We have established morphological diagrams on how colony patterns of bacterial species Escherichia coli and Pseudomonas aeruginosa change when environmental conditions vary. We have also studied the spatiotemporal change of cell density when periodic colony growth occurs. 2. We have investigated scaling properties, especially self-affinity, of growing interface of random patterns, by taking bacterial colonies and real landscapes as examples. 3. We have laid the foundation that the fundamental statistical aspects seen in complex systems in general are described by lognormal distributions, based on our observations of prefectural and municipal populations, our body height and weight, and so on.

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  • Interacting Infinite Particle Systems and Random Matrices

    Grant number：15540106  2003 - 2006

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)  CHIBA UNIVERSITY

    TANEMURA Hideki, NAKAGAMI Jyunichi, NAGISA Masaru, KONNO Norio, KATORI Makoto

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    Grant amount： \3300000 （ Direct Cost: \3300000 ）

    It is known that the distribution of particle positions in Dyson's model of Brownian motions coincides with that of eigenvalues of a Hermitian matrix-valued process, whose entries are independent Brownian motions. We considered a system of noncolliding Brownian motions, in which the noncolliding condition is imposed in a finite time interval (0,T]. This is a temporally inhomogeneous diffusion process and in the limit T to infinity, it converges to Dyson's model. We constructed such a Hermitian matrix-valued process that its eigenvalues are identically distributed with the particle positions of our system of noncolliding Brownian motions.
    As an extension of the theory of Dyson's models for the standard Gaussian random-matrix ensembles, we made a systematic study of hermitian matrix-valued processes. In addition to the noncolliding Brownian motions, we introduced noncolliding systems of generalized meanders and showed that all of the ten classes of eigenvalue statistics in the Altland-Zirnbauer classification are realized as particle distributions in the special cases of these diffusion particle systems.
    Then we proved that these non-colliding diffusions are Pfaffian processes, in the sense that any multitime correlation function is given by a Pfaffian. In the infinite particle limit, we showed that the elements of matrix kernels of the obtained infinite Pfaffian processes are generally expressed by the Riemann-Liouville differintegrals of functions comprising the Bessel functions.

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  • Research on the formation and fluctuation of random shapes in mathematical models of statistical mechanics

    Grant number：12440027  2000 - 2002

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)  KOBE UNIVERSITY

    HIGUCHI Yasunari, NAKANISHI Yasutaka, MIYAKAWA Tetsuro, FUKUYAMA Katsushi, MURAI Joushin, YAMAZAKI Tadashi

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    Grant amount： \10100000 （ Direct Cost: \10100000 ）

    1. We found a new proof of the fact that there are only two extremal Gibbs states for the two dimensional Ising model based on the percolation argument. As an application of this new method, we proved that there are only two extremal points of translationally invariant Gibbs states for the two dimensional Widom-Rowlinson model for sufficiently low temperatures.
    2. We gave an estimate of the speed of convergence for the time constant of the first passage Ising percolation for temperatures above the critical point.
    3. We proved a Dobrushin-Hryniv type limit theorem for the two-dimensional Widom-Rowlinson model. The conditions for the result to hold are a little relaxed.

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  • Researches on the diversity of growing patterns in biological systems

    Grant number：11214205  1999 - 2001

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research on Priority Areas (B)  Chuo University

    MATSUSHITA Mitsugu, KIMURA Masato, MIMURA Masayasu, KATORI Makoto

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    Grant amount： \13000000 （ Direct Cost: \13000000 ）

    Bacteria form characteristic and diverse colonies according to variation of environmental conditions such as nutrient concentration and substrate hardness. This implies that bacteria live actively by interacting collectively or multicellularly with their environment, instead of living unicellularly and passively. In order to elucidate this kind of collective behavior of biological organisms we have studied the growth mechanism and morphological change in colony formation of bacteria both microscopically and macroscopically. We have established morphological diagrams when varying both nutrient concentration and substrate softness. We have also elucidated the growth conditions and characteristics of various colony patterns for species Bacillus subtilis and Proteus mirabilis. Theoretically we have thoroughly investigated how well we can describe our experimental observations from the reaction-diffusion approach. All these results contribute not only to the study of colony formation of bacteria but also to the enlargement of experimental and theoretical studies on pattern formation of the population of biological organisms in general. The species Proteus mirabilis forms macroscopically almost perfect concentric-ring like colonies with approximately equal spacing by repeating collective migration and rest alternately. We have elucidated phenomenological mechanism for the repeated interface growth of the concentric-ring like colonies.

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  • Mathematical Physics

    2001 - 　

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    Grant type：Competitive

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  • 森林の林冠ギャップ空間分布の統計物理的研究

    Grant number：10874057  1998 - 2000

    日本学術振興会  科学研究費助成事業  萌芽的研究  中央大学

    香取 眞理

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    Grant amount： \2100000 （ Direct Cost: \2100000 ）

    1.森林総研の田中浩氏から提供していただいた小川森林保護区の航空写真による実測データに対して,我々が開発したイジングモデルによる解析方法を適用した.その際,パラメータを決定する新しい方法として,熱平衡状態で成立する相関等式を用いる方法を考案した.実際にこの方法を小川森林保護区の実測データの解析に応用すると,これまでのモンテカルロ法による方法ではパラメータを決定できなかった1991年のデータに対しても,パラメータを決定することが出来た.
    2.小川森林保護区の実測データでは,林冠ギャップの有無という2値のデータだけではなく,各サイトでの樹林の最高値が与えられている.このため,林冠ギャップと林冠とを分けるしきい値を変えた場合に,林冠ギャップ・クラスターの統計性がどのように変わるかを調べることも可能である.従来のモンテカルロ法によるパラメータ探索では,しきい値を変えるごとにモンテカルロ・シミュレーションを行わなければならなかったため,系統的なデータ解析は困難であった.しかし今回,熱平衡相関等式を用いる方法が出来たので,しきい値を変えて系統的に調べることが出来た.結果として,しきい値の選び方に依らず,決定されたパラメータはどれもイジングモデルの臨界値に近いものであった.
    3.森林動態に対する別の数理モデルとして,ある種の森林火災のパーコレーションモデルを提案し,計算機シミュレーションを行なった.そして,森林モデルで臨界性が実現される極限として知られているDrossel-Schwabl極限について考察した.
    4.有効グラフ上のパーコレーションの問題は,森林動態や伝染病伝播の問題の基礎モデルを作る上で重要である.この問題に対して,Arrowsmith-Essam公式と呼ばれるグラフ展開を拡張することが出来た.それにより,いわゆるフレンドリー・ウォークと呼ばれる相互作用する粒子系の統計力学を構成し,この系は高分子や,多成分流体系の「濡れ転移」のモデルと関連深いことを示した.

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  • 1次元粒子系の詳細釣合を満たさない定常分布の解明

    Grant number：06854015  1994 　 　

    日本学術振興会  科学研究費助成事業  奨励研究(A)  中央大学

    香取 眞理

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    Grant amount： \800000 （ Direct Cost: \800000 ）

    次のような研究を行った。
    (1)無限に拡がる格子上の無限個の粒子から成る系の定常分布を、これと“dual"な関係にある有限個の粒子から成る系を扱うことによって調べることができる場合がある。我々はGrayによってgraphical representationと呼ばれる方法で導入された、拡張されたdualityを別の方法によって再定式化した。これを応用して、拡張されたcontact processなどいくつかのモデルの臨界値を調べた。
    (2)クラスター間にランダムな競合があるようなdirected percolationを、計算機シミュレーションによって調べた。このような系は、臨界点においてself-affine性をもち、結晶成長系に対して提唱されていたMatsushita-Meakinのスケーリングが成立することが明かとなった。(磯上、松下両氏との共同研究。)
    (3)拡散を伴ったcontact processは、移住の効果も取り入れた伝染病伝播のモデルである。伝染病蔓延⇔撲滅の非平衡相転移の臨界値が、拡散率(移住の速さ)Dにどのように依存するかが問題となる。我々は、空間次元d【greater than or equal】3の場合に、臨界点の上限・下限を与えた。これにより、D→∞やd→∞で、平均場極限にどのように近づくかが明らかになった。crossover現象につ
    (4)非平衡臨界現象が見られるとき、その臨界値や臨界指数は、モデルの時間発展を与えるtransition matrixの固有値の、システムサイズL→∞での漸近形によって定められると考えられる。我々は、coalescing dualという関係にある2つのプロセスは、(各々のパラメーターの間にある関係が成り立つと)transition matrix自体は全く異なっていても、その固有値は任意のLにおいて総て等しくなることを証明した。このことは、coalescing dualの関係にあるプロセスは同じuniversality classに属することを示唆する。(乾、宇沢両氏との共同研究)。

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  • Study of the Ising Models Using Special Purpose Computer System

    Grant number：63302014  1988 - 1990

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Co-operative Research (A)  The University of Tokyo

    SUZUKI Masuo, KATORI Makoto, KATSURA Shigetoshi

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    Grant amount： \10000000 （ Direct Cost: \10000000 ）

    The computational physics becomes most important field in modern physics because the computational power has been increasing exponentially and computational study is most effective analyzing method for many important problems. It has been shown that the special purpose computer systems are useful for the theoretical researches. But such systems have not been available unless the researcher constructs one for his study. The main purpose of this research project is to supply such systems to the researchers who need strong simulation power for their studies for the Ising models.
    The special purpose computer system, named m-TIS2, has been developed in this research project. This machine is dedicated for the Monte Carlo simulation of the Ising models and it is the successor to our previous machine, m-TIS, which was developed in 1988. We have constructed thirteen m-TIS2 and have distributed them to the domestic collaborators. Therefore we have achieved the purpose of this project.
    The m-TIS2 has unique architecture. It uses the XILINX's LCA devices. And its hardware configuration can be modified easily by changing the configuration files written into the m-TIS2 at the beginning of the simulation. The fixed circuit is designed so that the m-TIS2 can hold maximum flexibility. Several configuration files are prepared for several models. For example, the CUBIC can simulate the two-dimensional models including up to the third neighbor interactions and three-dimensional models. The SG can treat <plus-minus>J spin-glass models. It is possible to make dedicated machine for different problems if some appropriate configuration files are prepare
    Our m-TIS and m-TIS2 are the first trial for the special purpose computer systems for theoretical sciences in Japan. And our project has been stimulating many other researches in these fields and several similar domestic projects have followed our project.

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  • Probability Theory

    1990 - 　

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    Grant type：Competitive

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  • Theoretical Research of Exotic Phase Transitions

    Grant number：63460035  1988 - 1989

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for General Scientific Research (B)  University of Tokyo

    SUZUKI Masuo, KATORI Makoto, MIYASHITA Seiji

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    Grant amount： \6400000 （ Direct Cost: \6400000 ）

    The research project "Theoretical Research of Exotic Phase Transitions" was performed by the support of the Grant-in-Aid from the Ministry of Education, Science and Culture during two fiscal years from april 1988.
    A general theory of phase transitions, so-called the coherent-anomaly method (CAM) and the super-effective-field theory have been developed to study exotic phase transitions such as spin glasses and chiral orders. It has been shown that there exists no phase transition in the two-dimensional <plus-minus>J Ising spin glass model, but that there exists a phase transition in three dimensions for the same model. The critical point T_<**> and the nonlinear susceptibility exponent gamma_* have been estimated as T_<**> <similar or equal> 1.4J/k_B and gamma_* <similar or equal> 3. Concerning the scalar chital order, it has been found, using the super-effective-field theory, to be quite difficult to occur in the two-dimensional antiferromagnetic Heisenberg model with cross bonds on a square lattice. This result agrees with other numerical studies.
    Suzuki has discovered a new scheme of "fractal path integrals". This is based on the following general decomposition theorem (Suzuki): e^<x(A+B)> = e^<t1A>e^<t2B>e^<t3A>e^<t4B>...e^<tNA> + O(x^<m+1>), for any positive integer m, where {t_j} are all real numbers proportional to x and they are fractal in their distribution. This new scheme including negative time or temperature is also conceptually interesting and it will be applicable to field theory and nuclear physics. In particular, this mew scheme of fractal decomposition of exponential operators is useful in quantum Monte Carlo simulations, if we combine this new approximant with the Trotter formula, because the resultant error becomes of the order of x^<m+1>n^<-m> for the Trotter number n.
    In order to make effective use of the CAM theory, Suzuki has devised the multi-effective- field theory and the confluent-transfer matrix method. The combination of the CAM theory with the former has given the estimate gamma <similar or equal> 1.7498 for the two-dimensional Ising m

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  • Phase Transitions and Critical Phenomena

    1985 - 　

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    Grant type：Competitive

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  • Statistical Physics

    1985 - 　

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    Grant type：Competitive

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Teaching Experience

  • 力学

  • 応用解析

  • 電磁気学

  • 量子力学

  • 統計力学

Committee Memberships

  • 2019.4 - 2021.3

    京都大学基礎物理学研究所   共同利用運営委員会議長団  

  • 2019.7 - 2019.12

    the Physical Society of Japan   Selection committee of the 1st Yonezawa Memorial Prize of the Physical Society of Japan  

  • 2009.9 - 2010.8

    日本物理学会   第65期理事  

  • 2008.9 - 2009.8

    日本物理学会   第64期理事  

  • 2001.9 - 2005.9

    日本物理学会   第57-58期代議員  

  • 2001.9 - 2003.8

    日本物理学会   学会誌新著紹介小委員会委員  

  • 2002.5 - 2003.4

    日本物理学会   統計力学・物性基礎論分科会世話人  

  • 1997.11 - 1999.10

    日本物理学会   学会誌新著紹介小委員会委員  

  • 1988.11 - 1991.9

    日本物理学会   学会誌新著紹介小委員会委員  

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