Updated on 2024/11/14

Information

 

写真a

 
TSUNODA KENKICHI
 
Organization
Faculty of Mathematics Division of Analysis Associate Professor
School of Sciences Department of Mathematics(Concurrent)
Graduate School of Mathematics Department of Mathematics(Concurrent)
Joint Graduate School of Mathematics for Innovation (Concurrent)
Title
Associate Professor
Contact information
メールアドレス
Profile
My research field is probability theory. In particular I am interested in problems related to so-called "Hydrodynamic limit", which is a certain type of space-time scaling limits. Hydrodynamic limit means a method which determines a macroscopic quantity of a microscopic system such as particles systems. To tackle a difficult problem related to Hydrodynamic limit, it is necessary to invoke results on functional analysis or partial differential equations, and to use specific arguments for particle systems and wide knowledge of probability theory. Hydrodynamic limit is formulated as Law of large numbers for a macroscopic quantity such as the number of particle systems or the current for a microscopic system. I am working on related Central limit theorem and Large deviation principle. In recent years, my another interest is Random topology, which has arisen from the development of Topological data analysis in applied mathematics. I am working on this new research area with my probabilistic technique although this theme is not related to above Hydrodynamic limit deeply.
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Research Areas

  • Natural Science / Basic mathematics

  • Natural Science / Applied mathematics and statistics

  • Natural Science / Basic analysis

Degree

  • Ph.D(mathematical science)

Research History

  • Kyushu University Faculty of Mathematics Department of Mathematical Science Associate Professor 

    2022.10 - Present

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  • 特定国立研究開発法人理化学研究所 革新知能統合研究センター 数理解析チーム 客員研究員 

    2018.3 - 2022.3

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    Country:Japan

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  • Osaka University 理学研究科数学専攻 Assistant Professor 

    2017.10 - 2022.9

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    Country:Japan

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  • 大阪大学理学研究科数学専攻助教 2017年10月〜2022年9月   

Research Interests・Research Keywords

  • Research theme: Probability Theory

    Keyword: Probability Theory

    Research period: 2024

  • Research theme: Scaling limit for an interacting particle system, especially, large deviation principle.

    Keyword: Probability theory, Interacting particle system, Hydrodynamic limit

    Research period: 2022.10

Awards

  • 2023年度日本数学会賞建部賢弘賞特別賞

    一般社団法人日本数学会   The 2023 MSJ Takebe Katahiro Prize

  • The 2023 MSJ Takebe Katahiro Prize

    一般社団法人日本数学会   Hydrodynamic limit and large deviation principle for lattice-gas

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Papers

  • Incompressible limit for weakly asymmetric simple exclusion processes coupled through collision Reviewed

    Patrick van Meurs, Kenkichi Tsunoda, Lu Xu

    Electronic Journal of Probability   29 ( none )   1 - 36   2024.1   ISSN:1083-6489

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    Publishing type:Research paper (scientific journal)   Publisher:Institute of Mathematical Statistics  

    DOI: 10.1214/24-ejp1225

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  • Large deviation principle for persistence diagrams of random cubical filtrations Reviewed

    Shu Kanazawa, Yasuaki Hiraoka, Jun Miyanaga, Kenkichi Tsunoda

    Journal of Applied and Computational Topology   8 ( 6 )   1649 - 1700   2024.1   ISSN:2367-1726 eISSN:2367-1734

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    Language:Others   Publishing type:Research paper (scientific journal)   Publisher:Springer Science and Business Media LLC  

    The objective of this article is to investigate the asymptotic behavior of the persistence diagrams of a random cubical filtration as the window size tends to infinity. Here, a random cubical filtration is an increasing family of random cubical sets, which are the union of randomly generated higher-dimensional unit cubes with integer coordinates in a Euclidean space. We first prove the strong law of large numbers for the persistence diagrams, inspired by the work of Hiraoka, Shirai, and Trinh, where the persistence diagram of a filtration of random geometric complexes is considered. As opposed to prior papers treating limit theorems for persistence diagrams, the present article aims to further study the large deviation behavior of persistence diagrams. We prove a large deviation principle for the persistence diagrams of a class of random cubical filtrations, and show that the rate function is given as the Fenchel–Legendre transform of the limiting logarithmic moment generating function. In the proof, we also establish a general method of lifting a large deviation principle for the tuples of persistent Betti numbers to persistence diagrams for broad applications.

    DOI: 10.1007/s41468-023-00161-6

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    Other Link: https://link.springer.com/article/10.1007/s41468-023-00161-6/fulltext.html

  • Motion by Mean Curvature from Glauber-Kawasaki Dynamics with Speed Change Reviewed

    Tadahisa Funaki, Patrick van Meurs, Sunder Sethuraman, Kenkichi Tsunoda

    Journal of Statistical Physics   190 ( 3 )   2023.1   ISSN:0022-4715 eISSN:1572-9613

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    Language:Others   Publishing type:Research paper (scientific journal)   Publisher:Springer Science and Business Media LLC  

    We derive a continuum mean-curvature flow as a certain hydrodynamic scaling limit of Glauber-Kawasaki dynamics with speed change. The Kawasaki part describes the movement of particles through particle interactions. It is speeded up in a diffusive space-time scaling. The Glauber part governs the creation and annihilation of particles. The Glauber part is set to favor two levels of particle density. It is also speeded up in time, but at a lesser rate than the Kawasaki part. Under this scaling, a mean-curvature interface flow emerges, with a homogenized ‘surface tension-mobility’ parameter reflecting microscopic rates. The interface separates the two levels of particle density. Similar hydrodynamic limits have been derived in two recent papers; one where the Kawasaki part describes simple nearest neighbor interactions, and one where the Kawasaki part is replaced by a zero-range process. We extend the main results of these two papers beyond nearest-neighbor interactions. The main novelty of our proof is the derivation of a ‘Boltzmann-Gibbs’ principle which covers a class of local particle interactions.

    DOI: 10.1007/s10955-022-03044-9

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    Other Link: https://link.springer.com/article/10.1007/s10955-022-03044-9/fulltext.html

  • Constant-speed interface flow from unbalanced Glauber-Kawasaki dynamics Reviewed

    Tadahisa Funaki, Patrick van Meurs, Sunder Sethuraman, Kenkichi Tsunoda

    Ensaios Matemáticos   38 ( 8 )   223 - 248   2023   eISSN:2175-0432

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    Publishing type:Research paper (scientific journal)   Publisher:Sociedade Brasileira de Matematica  

    DOI: 10.21711/217504322023/em388

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  • Glauber-Exclusion dynamics: rapid mixing regime Reviewed

    Ryokichi Tanaka, Kenkichi Tsunoda

    Electronic Journal of Probability   27 ( none )   2022.1   ISSN:1083-6489

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    Language:Others   Publishing type:Research paper (scientific journal)   Publisher:Institute of Mathematical Statistics  

    We show that for any attractive Glauber-Exclusion process on the one-dimensional lattice of size N with periodic boundary condition, if the corresponding hydrodynamic limit equation has a reaction term with a strictly convex potential, then the total-variation mixing time is of order O(log N). In particular, the result covers the full high-temperature regime in the original model introduced by De Masi, Ferrari and Lebowitz (1985).

    DOI: 10.1214/22-ejp865

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  • Exponentially slow mixing and hitting times of rare events for a reaction–diffusion model Reviewed

    Kenkichi Tsunoda

    Latin American Journal of Probability and Mathematical Statistics   19 ( 2 )   1161 - 1184   2022   ISSN:1980-0436

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Institute for Applied and Pure Mathematics (IMPA)  

    We consider the superposition of symmetric simple exclusion dynamics speeded-up in time, with spin-flip dynamics in a one-dimensional interval with periodic boundary conditions. We show that the mixing time has an exponential lower bound in the system size if the potential of the hydrodynamic equation has two or more local minima. We also apply our estimates to show that the normalized hitting times of rare events converge to a mean one exponential random variable if the potential has a unique minimum

    DOI: 10.30757/alea.v19-48

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  • Derivation of viscous Burgers equations from weakly asymmetric exclusion processes Reviewed

    M. Jara, C. Landim, K. Tsunoda

    Annales de l'Institut Henri Poincaré, Probabilités et Statistiques   57 ( 1 )   169 - 194   2021.2

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

    DOI: 10.1214/20-aihp1075

  • Hydrostatic limit for exclusion process with slow boundary revisited Reviewed International journal

    K. Tsunoda

    RIMS Kôkyûroku Bessatsu   B79   149 - 162   2020.1

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

  • Motion by Mean Curvature from Glauber-Kawasaki Dynamics Reviewed

    Tadahisa Funaki, Kenkichi Tsunoda

    JOURNAL OF STATISTICAL PHYSICS   177 ( 2 )   183 - 208   2019.10

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

    We study the hydrodynamic scaling limit for the Glauber-Kawasaki dynamics. It is known that, if the Kawasaki part is speeded up in a diffusive space-time scaling, one can derive the Allen-Cahn equation which is a kind of the reaction-diffusion equation in the limit. This paper concerns the scaling that the Glauber part, which governs the creation and annihilation of particles, is also speeded up but slower than the Kawasaki part. Under such scaling, we derive directly from the particle system the motion by mean curvature for the interfaces separating sparse and dense regions of particles as a combination of the hydrodynamic and sharp interface limits.

    DOI: 10.1007/s10955-019-02364-7

  • Static large deviations for a reaction–diffusion model Reviewed

    J. Farfán, C. Landim, K. Tsunoda

    Probability Theory and Related Fields   174 ( 1-2 )   49 - 101   2019.6

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

    DOI: 10.1007/s00440-018-0858-5

  • Strong Law of Large Numbers for Betti Numbers in the Thermodynamic Regime Reviewed

    Akshay Goel, Khanh Duy Trinh, Kenkichi Tsunoda

    JOURNAL OF STATISTICAL PHYSICS   174 ( 4 )   865 - 892   2019.2

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

    We establish the strong law of large numbers for Betti numbers of random ech complexes built on RN-valued binomial point processes and related Poisson point processes in the thermodynamic regime. Here we consider both the case where the underlying distribution of the point processes is absolutely continuous with respect to the Lebesgue measure on RN and the case where it is supported on a C1 compact manifold of dimension strictly less than N. The strong law is proved under very mild assumption which only requires that the common probability density function belongs to Lp spaces, for all 1p<.

    DOI: 10.1007/s10955-018-2201-z

  • Limit Theorems for Random Cubical Homology Reviewed

    Yasuaki Hiraoka, Kenkichi Tsunoda

    DISCRETE & COMPUTATIONAL GEOMETRY   60 ( 3 )   665 - 687   2018.10

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

    This paper studies random cubical sets in R-d. Given a cubical set X. R-d, a random variable.Q. [0, 1] is assigned for each elementary cube Q in X, and a random cubical set X(t) is defined by the sublevel set of X consisting of elementary cubes with.Q <= t for each t. [0, 1]. Under this setting, the main results of this paper show the limit theorems (law of large numbers and central limit theorem) for Betti numbers and lifetime sums of random cubical sets and filtrations. In addition to the limit theorems, the positivity of the limiting Betti numbers is also shown.

    DOI: 10.1007/s00454-018-0007-z

  • Hydrostatics and dynamical large deviations for a reaction-diffusion model Reviewed

    C. Landim, K. Tsunoda

    Annales de l'Institut Henri Poincaré, Probabilités et Statistiques   54 ( 1 )   51 - 74   2018.2

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

    DOI: 10.1214/16-aihp794

  • Hydrodynamic limit for a certain class of two-species zero-range processes Reviewed

    Kenkichi Tsunoda

    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN   68 ( 2 )   885 - 898   2016.4

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

    Grosskinsky and Spohn [5] studied several-species zero-range processes and gave a necessary and sufficient condition for translation invariant measures to be invariant under such processes. Based on this result, they investigated the hydrodynamic limit. In this paper, we consider a certain class of two-species zero-range processes which are outside of the family treated by Grosskinsky and Spohn. We prove a homogenization property for a tagged particle and apply it to derive the hydrodynamic limit under the diffusive scaling.

    DOI: 10.2969/jmsj/06820885

  • Scaling limits for Glauber-Kawasaki processes Reviewed International journal

    K. Tsunoda

    RIMS Kôkyûroku Bessatsu   B59   45 - 56   2016.1

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

  • Metastability of Reversible Random Walks in Potential Fields Reviewed

    C. Landim, R. Misturini, K. Tsunoda

    JOURNAL OF STATISTICAL PHYSICS   160 ( 6 )   1449 - 1482   2015.9

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

    Let Xi be an open and bounded subset of , and let F ; Xi -> R be a twice continuously differentiable function. Denote by the discretization of Xi, Xi(N) = Xi boolean AND and denote by the continuous-time, nearest-neighbor, random walk on which jumps from to at rate . We examine in this article the metastable behavior of among the wells of the potential F.

    DOI: 10.1007/s10955-015-1298-6

  • Derivation of a free boundary problem from an exclusion process with speed change Invited Reviewed International journal

    K. Tsunoda

    Markov Processes Relat. Fields   21   263 - 273   2015.1

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

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Presentations

  • Sharp interface limit for a quasi-linear large deviation rate function International conference

    Kenkichi Tsunoda

    Interacting particle systems and stochastic analysis  2024.3 

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    Event date: 2024.5

    Language:English  

    Country:Japan  

  • Scaling limits for Glauber-Kawasaki process International conference

    Kenkichi Tsunoda

    The 13th AIMS conference on dynamical systems, differential equations and applications  2023.6 

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    Event date: 2024.5

    Language:English  

    Country:Japan  

  • Scaling limits for Glauber-Kawasaki process International conference

    Kenkichi Tsunoda

    11th International conference on stochastic analysis and its applications  2023.6 

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    Event date: 2024.5

    Language:English  

    Country:Japan  

  • Sharp interface limit for Glauber-Kawasaki process International conference

    Kenkichi Tsunoda

    Stochastic processes and related fields  2023.9 

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    Event date: 2024.5

    Language:English  

    Country:Japan  

  • 反応拡散模型に対するスケール極限

    角田 謙吉

    東北確率論セミナー  2023.11 

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    Event date: 2024.5

    Language:Japanese  

    Country:Japan  

  • Incompressible limit for a weakly asymmetric simple exclusion process with collision International conference

    Kenkichi Tsunoda

    Random interacting systems, scaling limits, and universality  2023.12 

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    Event date: 2024.5

    Language:English  

    Country:Japan  

  • 流体力学極限に対する大偏差原理

    角田 謙吉

    九州大学数理談話会  2023.12 

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    Event date: 2024.5

    Language:Japanese  

    Country:Japan  

  • Glauber+Kawasaki過程のレート関数に対する特異極限

    角田 謙吉

    2023年度確率論シンポジウム  2023.12 

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    Event date: 2024.5

    Language:Japanese  

    Country:Japan  

  • Large deviations for random graphs

    角田 謙吉

    無限粒子系、確率場の諸問題XVIII  2024.1 

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    Event date: 2024.5

    Language:Japanese  

    Country:Japan  

  • Sharp Interface Limit for Glauber-Kawasaki Process International conference

    Kenkichi Tsunoda

    French Japanese conference on probability & interactions, Institut des Hautes Études Scientifiques  2024.3 

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    Event date: 2024.5

    Language:English  

    Country:Japan  

  • Large deviations for random cubical filtrations

    角田 謙吉

    無限粒子系、確率場の諸問題XVII  2023.1 

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    Event date: 2023.5

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    Country:Japan  

  • Mixing time for a reaction-diffusion model International conference

    Kenkichi Tsunoda

    Ninth Bielefeld-SNU Joint Workshop in Mathematics  2022.5 

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    Event date: 2023.5

    Language:English  

    Country:Japan  

  • Occupation time large deviations for one-dimensional zero-range process

    角田 謙吉

    関西確率論セミナー  2022.10 

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    Event date: 2023.5

    Language:Japanese  

    Country:Japan  

  • Large deviation principle for persistence diagrams of random cubical filtrations

    角田 謙吉

    確率論シンポジウム  2022.12 

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    Event date: 2023.5

    Language:Japanese  

    Country:Japan  

  • Large deviations and mixing times for a reaction-diffusion model International conference

    Kenkichi Tsunoda

    Seminário de Probabilidade e Mecânica Estatística  2022.10 

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    Event date: 2022.10

    Language:English  

    Country:Japan  

  • Occupation time large deviations for one-dimensional zero-range process International conference

    Kenkichi Tsunoda

    Symposium on interacting stochastic systems  2022.6 

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    Event date: 2022.10

    Language:English  

    Country:Japan  

  • 1次元零距離過程の占有時間に対する大偏差原理

    角田 謙吉

    九州確率論セミナー  2022.10 

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    Event date: 2022.10

    Language:Japanese  

    Country:Japan  

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MISC

  • パーシステントホモロジーと確率論(特集◎トポロジカルデータ解析の拡がり) 数理科学 サイエンス社 Reviewed

    角田謙吉

    2023.6

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    Language:Japanese  

  • 粒子系・界面成長モデルからKPZ普遍性(特集◎統計力学の視点で捉える確率論) 数理科学 サイエンス社 Reviewed

    角田謙吉

    2023.3

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    Language:Japanese  

Professional Memberships

  • THE MATHEMATICAL SOCIETY OF JAPAN

    2016 - Present

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  • The Mathematical Society of Japan

  • THE MATHEMATICAL SOCIETY OF JAPAN

Academic Activities

  • Organizer International contribution

    21st Stochastic analysis on large scale interacting systems  ( RIMS, Kyoto University Japan ) 2023.10

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    Type:Competition, symposium, etc. 

  • Organizer International contribution

    Workshop on probabilistic methods in statistical mechanics of random media and random fields 2023  ( Nishijin Plaza, Kyushu University Japan ) 2023.1

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    Type:Competition, symposium, etc. 

  • 世話人

    20th Stochastic analysis on large scale interacting systems  ( Japan ) 2022.12

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    Type:Competition, symposium, etc. 

  • RIMS Kôkyûroku Bessatsu B79: Stochastic Analysis on Large Scale Interacting Systems eds. Ryoki Fukushima, Tadahisa Funaki, Yukio Nagahata, Hirofumi Osada, Kenkichi Tsunoda

    2022.10

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    Type:Academic society, research group, etc. 

  • 世話人

    2021年度確率論シンポジウム  ( Japan ) 2021.12

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    Type:Competition, symposium, etc. 

  • 世話人

    19th Stochastic analysis on large scale interacting systems  ( Japan ) 2021.12

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    Type:Competition, symposium, etc. 

  • 世話人

    18th Stochastic analysis on large scale interacting systems  ( Japan ) 2019.11

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    Type:Competition, symposium, etc. 

  • Organizer International contribution

    17th Stochastic analysis on large scale interacting systems  ( RIMS, Kyoto University Japan ) 2018.11

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    Type:Competition, symposium, etc. 

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Research Projects

  • Large deviation principle and metastability for lattice gas

    Grant number:22K13929  2022 - 2025

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Early-Career Scientists

    角田 謙吉

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    Authorship:Principal investigator  Grant type:Scientific research funding

    流体力学極限は確率論の枠組みの中で大数の法則として定式化され、関連するスケール極限である大偏差原理や、より詳細に系の振る舞いを記述する準安定性の問題が自然に考えられる。微視的な系は振動子鎖模型や界面模型等さまざまなものが考えられるが、本研究では格子気体とよばれる確率的粒子系に焦点を当て、その例である零距離過程とグラウバー+川崎過程を扱い、本研究では零距離過程に対する大偏差原理及びグラウバー+川崎過程に対する準安定性について研究を行う。

    CiNii Research

  • Limit theorems for stationary nonequilibrium states

    Grant number:18K13426  2018 - 2021

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Early-Career Scientists

    Tsunoda Kenkichi

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    Authorship:Principal investigator  Grant type:Scientific research funding

    I studied a scaling limit for a lattice gas. Especially, I studied a hydrodynamic limit and problems related to a large deviation principle. I obtained results on law of large numbers for a stationary state of an exclusion process with slow boundary, derivation of the mean curvature flow from a Glauber-Kawasaki dynamics, derivation of the Burgers equation from a weakly asymmetric exclusion process and phase transition in mixing times for a Glauber-Kawasaki dynamics.

    CiNii Research

  • 非平衡定常状態の流体力学極限に対する大偏差原理による解析

    Grant number:16H07041  2016 - 2017

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Research Activity start-up

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    Authorship:Principal investigator  Grant type:Scientific research funding

Educational Activities

  • 学部・大学院教育では確率論に関連する講義を主に担当している。

Class subject

  • 確率論基礎・演習

    2024.10 - 2025.3   Second semester

  • 微分積分学Ⅱ

    2024.10 - 2025.3   Second semester

  • 数学演習AⅡ

    2024.10 - 2025.3   Second semester

  • 確率論大意

    2024.4 - 2024.9   First semester

  • 数学演習AⅠ

    2024.4 - 2024.9   First semester

  • 微分積分学Ⅰ

    2024.4 - 2024.9   First semester

  • 数学特論10

    2024.4 - 2024.9   First semester

  • 微分積分学Ⅱ

    2023.10 - 2024.3   Second semester

  • 微分積分学Ⅱ

    2023.10 - 2024.3   Second semester

  • 数理科学特別講義Ⅳ

    2023.4 - 2023.9   First semester

  • 確率論大意

    2023.4 - 2023.9   First semester

  • 微分積分学Ⅰ

    2023.4 - 2023.9   First semester

  • 微分積分学Ⅰ

    2023.4 - 2023.9   First semester

  • 数学特論10

    2023.4 - 2023.9   First semester

  • コアセミナーⅠ

    2023.4 - 2023.9   First semester

  • 数理科学特論4

    2023.4 - 2023.9   First semester

  • 数学特論10(確率論)

    2022.10 - 2023.3   Second semester

  • 確率論大意

    2022.10 - 2023.3   Second semester

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FD Participation

  • 2023.8   Role:Participation   Title:数理学府FD

    Organizer:[Undergraduate school/graduate school/graduate faculty]

  • 2023.4   Role:Participation   Title:令和5年度 第1回全学FD(新任教員の研修)The 1st All-University FD (training for new faculty members) in FY2023

    Organizer:University-wide