Updated on 2024/11/14

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.
Homepage
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

    　 More details

  • 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

    　 More details

    Country：Japan

    researchmap

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

    2017.10 - 2022.9

    　 More details

    Country：Japan

    researchmap

  • 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

    　More details

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 ）

    　More details

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

    DOI： 10.1214/24-ejp1225

    researchmap

  • 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 ）

    　More details

    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

    Scopus

    researchmap

    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 ）

    　More details

    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

    Web of Science

    Scopus

    researchmap

    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 ）

    　More details

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

    DOI： 10.21711/217504322023/em388

    researchmap

  • Glauber-Exclusion dynamics: rapid mixing regime Reviewed

    Ryokichi Tanaka, Kenkichi Tsunoda

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

    　More details

    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

    Scopus

    researchmap

▼display all

Presentations

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

    Kenkichi Tsunoda

    Interacting particle systems and stochastic analysis  2024.3 

    　More details

    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 

    　More details

    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 

    　More details

    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 

    　More details

    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 

    　More details

    Event date： 2024.5

    Language：Japanese  

    Country：Japan  

▼display all

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

    　More details

    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

    　More details

    Language：Japanese  

Professional Memberships

  • THE MATHEMATICAL SOCIETY OF JAPAN

    2016 - Present

    　 More details

  • 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

    　More details

    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

    　More details

    Type：Competition, symposium, etc. 

  • 世話人

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

    　More details

    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

    　More details

    Type：Academic society, research group, etc. 

  • 世話人

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

    　More details

    Type：Competition, symposium, etc. 

▼display all

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

    　 More details

    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

    　 More details

    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

    　 More details

    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

▼display all

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