Faculty Profiles - TSUNODA KENKICHI

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）

Contact information

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.

Homepage

https://www3.math.kyushu-u.ac.jp/~tsunoda/

External link

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

Web of Science

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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

Language：Japanese

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

数学演習ＡⅡ

2024.10 - 2025.3 Second semester
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
数学特論１０

2024.4 - 2024.9 First 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
微分積分学Ⅱ

2023.10 - 2024.3 Second semester
微分積分学Ⅱ

2023.10 - 2024.3 Second semester
数理科学特論４

2023.4 - 2023.9 First 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