Studies on large scale interacting systems and related stochastic partial differential equations

• Project/Area Number: 18H03672
• Research Category: Grant-in-Aid for Scientific Research (A)
• Allocation Type: Single-year Grants
• Section: 一般
• Review Section: Medium-sized Section 12:Analysis, applied mathematics, and related fields
• Research Institution: The University of Tokyo (2022); Waseda University (2018-2021)
• Principal Investigator: 舟木 直久 東京大学, 大学院数理科学研究科, 名誉教授 (60112174)
• Co-Investigator(Kenkyū-buntansha): 佐々田 槙子 東京大学, 大学院数理科学研究科, 准教授 (00609042) ; 長田 博文 中部大学, 工学部, 教授 (20177207) ; 福島 竜輝 筑波大学, 数理物質系, 准教授 (60527886) ; 笹本 智弘 東京工業大学, 理学院, 教授 (70332640)
• Project Period (FY): 2018-04-01 – 2023-03-31
• Project Status: Granted (Fiscal Year 2022)
• Budget Amount: ¥41,990,000 (Direct Cost: ¥32,300,000、Indirect Cost: ¥9,690,000); Fiscal Year 2022: ¥8,450,000 (Direct Cost: ¥6,500,000、Indirect Cost: ¥1,950,000); Fiscal Year 2021: ¥8,320,000 (Direct Cost: ¥6,400,000、Indirect Cost: ¥1,920,000); Fiscal Year 2020: ¥7,930,000 (Direct Cost: ¥6,100,000、Indirect Cost: ¥1,830,000); Fiscal Year 2019: ¥8,060,000 (Direct Cost: ¥6,200,000、Indirect Cost: ¥1,860,000); Fiscal Year 2018: ¥9,230,000 (Direct Cost: ¥7,100,000、Indirect Cost: ¥2,130,000)
• Keywords: 確率論 / 解析学 / 統計力学 / 数理物理 / 関数方程式

Outline of Annual Research Achievements

大規模相互作用系とは、もともと統計物理学の研究において用いられる各種の数理モデルの総称であり、莫大な自由度を持つ系である。以下、本年度の研究実績からいくつか具体的に述べる。本研究は、研究代表者と研究分担者らの緊密な協力の下に進められたが、研究実績は各テーマを主導した研究者ごとに述べる。
研究代表者の舟木は、ランダム環境内の相互作用粒子系の極限として自然に得られる放物型確率偏微分方程式について、パラコントロール解析に基づき、まず一般化した状況の下で、解の定式化を行い、局所解の存在と一意性を示した。また、３次元ヤング図形の時間発展モデルに対する大偏差原理の研究を行った。
分担者の長田は、長年取り組んできた無限次元確率微分方程式の強解の存在と一意性に関する研究を完成し出版した。この結果を応用することにより、ディリクレ形式の一意性を証明した。分担者の笹本は、Arndt-Heinzel-Rittenbergモデルと呼ばれる、２成分排他過程の揺らぎに関する研究を進めた。その結果、ある初期条件の場合に対し、２成分粒子のカレントの原点における結合分布が多重積分で表せることを示し、その漸近解析を行うことに成功した。また、KPZ系を有限温度自由フェルミオンと関係付ける研究を進めた。分担者の福島は、ランダム媒質中のランダムウォークに関して漸近速度や熱核評価、局在する際の極限分布など幅広く研究を行なった。また向きのついた高分子模型の大偏差原理の研究を行なった。分担者の佐々田は、非勾配型モデルに対する流体力学極限を一般的に扱うための枠組みを構築し、特にその証明で鍵となる閉形式の分解定理の新しい定式化を行った。これにより、分解定理における群作用と保存量の役割が、数学的に厳密な形で明らかになった。

Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

令和二年度の交付申請書で主な研究目標として掲げたのは次の３点である。(1)ランダム場中の偏微分方程式に対する極限定理を、近年大きな展開を見せている特異な確率偏微分方程式の理論であるパラコントロール解析を用いて考察する。(2)確率的６頂点模型のKPZ極限についてパラコントロール解析による考察を行い、その一般化を目指す。(3)保存則を持つ確率Allen-Cahn方程式の３つの異なる時間スケールについて調べる。
このうち(1)の目標は達成され、さらに長時間挙動の解析へと発展している。(2)については確率的６頂点模型の拡張として、粒子の生成・消滅を許す確率的８頂点模型の導入へと進展した。(3)は、関連する相互作用粒子系の観点からの研究が進行している。

Strategy for Future Research Activity

上記「８. 現在までの進捗状況」でも述べたが、確率的６頂点模型の拡張として確率的８頂点模型を新たに導入した。その不変測度、流体力学極限、線形揺動、非線形揺動について調べる予定である。ランダム環境内の相互作用粒子系の極限として得られる放物型非線形確率偏微分方程式については、長時間挙動の解析を進め研究を完成させたいと考えている。

Research Products

• [Int'l Joint Research] パリ-サクレー大学(フランス)
• [Int'l Joint Research] アリゾナ大学/ペンシルバニア大学/シカゴ大学(米国)
• [Int'l Joint Research] ベルリン工科大学(ドイツ)
• [Int'l Joint Research] メルボルン大学(オーストラリア)
• [Int'l Joint Research] シンガポール国立大学(シンガポール)
• [Int'l Joint Research]
• [Int'l Joint Research] Ecole Normale Superieure de Cachan/Univ Paris-Sud/Univ. Cote D'azur (Nice)(フランス)
• [Int'l Joint Research] Gran Sasso Science Institute/Univ L'Aquila(イタリア)
• [Int'l Joint Research] Univ Federal Rio de Janeiro(ブラジル)
• [Int'l Joint Research] Univ Arizona(米国)
• [Int'l Joint Research] Technical University of Munich(ドイツ)
• [Int'l Joint Research]
• [Int'l Joint Research] Ecole Normale Superieure de Cachan/Univ Paris-Sud/Univ. Cote D'azur(フランス)
• [Int'l Joint Research] Univ Arizona/UCLA/Stanford Univ(米国)
• [Int'l Joint Research] Univ L'Aquila/Gran Sasso Science Institute(イタリア)
• [Int'l Joint Research] Weierstrass institute/Technical Univ Berlin(ドイツ)
• [Int'l Joint Research] Melbourne Univ(オーストラリア)
• [Int'l Joint Research]
• [Journal Article] Uniqueness of Dirichlet Forms Related to Infinite Systems of Interacting Brownian Motions (2021)
  • Author(s): Kawamoto Yosuke、Osada Hirofumi、Tanemura Hideki
  • Journal Title: Potential Anal. Volume: - Pages: 639-676
  • DOI: 10.1007/s11118-020-09872-2
  • Peer Reviewed / Open Access
• [Journal Article] Distribution of the random walk conditioned on survival among quenched Bernoulli obstacles (2021)
  • Author(s): Ding Jian、Fukushima Ryoki、Sun Rongfeng、Xu Changji
  • Journal Title: The Annals of Probability Volume: 49 Pages: 206-243
  • DOI: 10.1214/20-aop1450
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] On large deviation rate functions for a continuous-time directed polymer in weak disorder (2021)
  • Author(s): Fukushima Ryoki、Junk Stefan
  • Journal Title: Electronic Communications in Probability Volume: 26 Pages: 1-10
  • DOI: 10.1214/21-ecp378
  • NAID: 120007190970
  • Peer Reviewed / Open Access
• [Journal Article] Existence and uniqueness of the entropy solution of a stochastic conservation law with a Q‐Brownian motion (2020)
  • Author(s): Funaki Tadahisa、Gao Yueyuan、Hilhorst Danielle
  • Journal Title: Mathematical Methods in the Applied Sciences Volume: 43 Pages: 5860-5886
  • DOI: 10.1002/mma.6329
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Infinite-dimensional stochastic differential equations and tail σ-fields (2020)
  • Author(s): Osada Hirofumi、Tanemura Hideki
  • Journal Title: Probability Theory and Related Fields Volume: 177-3-4 Pages: 1137-1242
  • DOI: 10.1007/s00440-020-00981-y
  • Peer Reviewed / Open Access
• [Journal Article] Stationary Higher Spin Six Vertex Model and q-Whittaker measure (2020)
  • Author(s): Takashi Imamura, Matteo Mucciconi, Tomohiro Sasamoto
  • Journal Title: Probability Theory and Related Fields Volume: -- Pages: 923-1042
  • DOI: 10.1007/s00440-020-00966-x
  • Peer Reviewed
• [Journal Article] New high-dimensional examples of ballistic random walks in random environment (2020)
  • Author(s): Ryoki Fukushima, Alejandro F. Ramirez
  • Journal Title: RIMS Kokyuroku Bessatsu Volume: B79 Pages: 109-122
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Geometry of the random walk range conditioned on survival among Bernoulli obstacles (2020)
  • Author(s): Ding Jian、Fukushima Ryoki、Sun Rongfeng、Xu Changji
  • Journal Title: Probability Theory and Related Fields Volume: 177 Pages: 91-145
  • DOI: 10.1007/s00440-019-00943-z
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Biased Random Walk Conditioned on Survival Among Bernoulli Obstacles: Subcritical Phase (2020)
  • Author(s): Ding Jian、Fukushima Ryoki、Sun Rongfeng、Xu Changji
  • Journal Title: Communications in Mathematical Physics Volume: 376 Pages: 2161-2195
  • DOI: 10.1007/s00220-019-03644-9
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Quenched tail estimate for the random walk in random scenery and in random layered conductance II (2020)
  • Author(s): Deuschel Jean-Dominique、Fukushima Ryoki
  • Journal Title: Electronic Journal of Probability Volume: 25 Pages: 1-28
  • DOI: 10.1214/20-ejp478
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Duality between box-ball systems of finite box and/or carrier capacity (2020)
  • Author(s): D. A. Croydon and M. Sasada
  • Journal Title: RIMS Kokyuroku Bessatsu Volume: B79 Pages: 63-107
  • Peer Reviewed / Open Access
• [Journal Article] Dynamics of the ultra-discrete Toda lattice via Pitman's transformation (2020)
  • Author(s): D. A. Croydon, M. Sasada and S. Tsujimoto
  • Journal Title: RIMS Kokyuroku Bessatsu Volume: B78 Pages: 235-250
  • Peer Reviewed / Open Access
• [Journal Article] Hydrodynamic limit for a facilitated exclusion process (2020)
  • Author(s): Blondel Oriane、Erignoux Cl?ment、Sasada Makiko、Simon Marielle
  • Journal Title: Annales de l'Institut Henri Poincare, Probabilites et Statistiques Volume: 56 Pages: 667-714
  • DOI: 10.1214/19-aihp977
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Invariant measures in coupled KPZ equations (2019)
  • Author(s): T. Funaki
  • Journal Title: Stochastic Dynamics Out of Equilibrium (Book) Volume: 印刷中 Pages: 560-568
  • DOI: 10.1007/978-3-030-15096-9_20
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Motion by Mean Curvature from Glauber-Kawasaki Dynamics (2019)
  • Author(s): Funaki, T., Tsunoda, K.
  • Journal Title: Journal of Statistical Physics Volume: 177 Pages: 183-208
  • DOI: 10.1007/s10955-019-02364-7
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Fast-reaction limit for Glauber-Kawasaki dynamics with two components (2019)
  • Author(s): De Masi A.、Funaki T.、Presutti E.、Vares M. E.
  • Journal Title: Alea (Rio de Janeiro) Volume: 16 Pages: 957-957
  • DOI: 10.30757/alea.v16-34
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Dynamical Bulk Scaling Limit of Gaussian Unitary Ensembles and Stochastic Differential Equation Gaps (2019)
  • Author(s): Kawamoto Yosuke、Osada Hirofumi
  • Journal Title: Journal of Theoretical Probability Volume: - Pages: 1-27
  • DOI: 10.1007/s10959-018-0816-2
  • Peer Reviewed / Open Access
• [Journal Article] 無限粒子系の確率解析学: --古典的確率解析の新展開とランダム行列の力学的普遍性-- (2019)
  • Author(s): 長田博文
  • Journal Title: 数学（岩波書店） Volume: 70
  • NAID: 130008029703
  • Peer Reviewed
• [Journal Article] The logarithmic derivative for point processes with equivalent Palm measures (2019)
  • Author(s): A. I. Bufetov, A. V. Dymov, H. Osada
  • Journal Title: J. Math. Soc. Japan Volume: 71 Issue: 2 Pages: 451-469
  • DOI: 10.2969/jmsj/78397839
  • NAID: 130007636389
  • ISSN: 0025-5645, 1881-1167, 1881-2333
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Exact large deviation function of spin current for the one dimensional XX spin chain with domain wall initial condition (2019)
  • Author(s): Hiroki Moriya, Rikuo Nagao, Tomohiro Sasamoto,
  • Journal Title: Journal of Statistical Mechanics: Theory and Experiment Volume: 2019 Pages: 063105-063105
  • DOI: 10.1088/1742-5468/ab1dd6
  • Peer Reviewed
• [Journal Article] Zero temperature limit for the Brownian directed polymer among Poissonian disasters (2019)
  • Author(s): Fukushima Ryoki、Junk Stefan
  • Journal Title: The Annals of Applied Probability Volume: 29 Pages: 3821-3860
  • DOI: 10.1214/19-aap1493
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Invariant measures for the box-ball system based on stationary Markov chains and periodic Gibbs measures (2019)
  • Author(s): Croydon David A.、Sasada Makiko
  • Journal Title: Journal of Mathematical Physics Volume: 60 Pages: 083301-083301
  • DOI: 10.1063/1.5095622
  • Peer Reviewed / Open Access
• [Journal Article] 5/6-Superdiffusion of Energy for Coupled Charged Harmonic Oscillators in a Magnetic Field (2019)
  • Author(s): Saito Keiji、Sasada Makiko、Suda Hayate
  • Journal Title: Communications in Mathematical Physics Volume: 372 Pages: 151-182
  • DOI: 10.1007/s00220-019-03506-4
  • Peer Reviewed
• [Journal Article] Sharp interface limit for stochastically perturbed mass conserving Allen?Cahn equation (2019)
  • Author(s): Funaki Tadahisa、Yokoyama Satoshi
  • Journal Title: Annals of Probability Volume: 47 Pages: 560-612
  • DOI: 10.1214/18-aop1268
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] 長田博文氏の業績---長距離相互作用を持つ無限粒子系の確率解析--- (2019)
  • Author(s): 舟木直久
  • Journal Title: 数学 Volume: 71 Pages: 202-209
  • NAID: 130008029692
  • Peer Reviewed
• [Journal Article] Quenched tail estimate for the random walk in random scenery and in random layered conductance (2019)
  • Author(s): Deuschel Jean-Dominique、Fukushima Ryoki
  • Journal Title: Stochastic Processes and their Applications Volume: 129 Pages: 102-128
  • DOI: 10.1016/j.spa.2018.02.011
  • NAID: 120006644057
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Variational discretization for the nonlequilibrium thermodynamics of simple system (2018)
  • Author(s): Francois Gay-Balmaz and Hiroaki Yoshimura
  • Journal Title: Stochastic Partial Differential Equations and Related Fields Volume: 31 Pages: 1673-1705
  • DOI: 10.1007/978-3-319-74929-7_6
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Convergence of a finite volume scheme for a stochastic conservation law involving a Q-Brownian motion (2018)
  • Author(s): T. Funaki, Y. Gao and D. Hilhorst
  • Journal Title: Discrete & Continuous Dynamical Systems - B Volume: 23 Pages: 1459-1502
  • DOI: 10.3934/dcdsb.2018159
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Hydrodynamic Limit for Exclusion Processes (2018)
  • Author(s): Funaki Tadahisa
  • Journal Title: Communications in Mathematics and Statistics Volume: 6 Pages: 417-480
  • DOI: 10.1007/s40304-018-0161-x
  • Peer Reviewed
• [Journal Article] Finite particle approximations of interacting Brownian particles with logarithmic potentials (2018)
  • Author(s): Yosuke Kawamoto, Hirofumi Osada
  • Journal Title: J. Math. Soc. Japan Volume: 70 Pages: 921-952
  • Peer Reviewed
• [Journal Article] Infinite-dimensional Stochastic Differential Equations with Symmetry (2018)
  • Author(s): H. Osada
  • Journal Title: Stochastic Partial Differential Equations and Related Fields Volume: 229 Pages: 549-559
  • Peer Reviewed
• [Journal Article] Transient Dynamics of Double Quantum Dots Coupled to Two Reservoirs (2018)
  • Author(s): Takahisa Fukadai, and Tomohiro Sasamoto
  • Journal Title: J. Phys. Soc. Jpn. Volume: 87 Issue: 5 Pages: 054006-054006
  • DOI: 10.7566/jpsj.87.054006
  • NAID: 210000134814
  • ISSN: 0031-9015, 1347-4073
  • Peer Reviewed
• [Journal Article] Exact Confirmation of 1D Nonlinear Fluctuating Hydrodynamics for a Two-Species Exclusion Process (2018)
  • Author(s): Chen Zeying、de Gier Jan、Hiki Iori、Sasamoto Tomohiro
  • Journal Title: Physical Review Letters Volume: 120 Pages: 240601-240601
  • DOI: 10.1103/physrevlett.120.240601
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Eigenvalue Fluctuations for Lattice Anderson Hamiltonians: Unbounded Potentials (2018)
  • Author(s): BISKUP Marek、FUKUSHIMA Ryoki、K?NIG Wolfgang
  • Journal Title: IIS Volume: 24 Issue: 1 Pages: 59-76
  • DOI: 10.4036/iis.2018.a.03 10.4036/iis.2018.A.03
  • NAID: 130007412788
  • ISSN: 1340-9050, 1347-6157
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Slowdown estimates for one-dimensional random walks in random environment with holding times (2018)
  • Author(s): Amir Dembo、Ryoki Fukushima、Naoki Kubota
  • Journal Title: Electronic Communications in Probability Volume: 23 Pages: 1-12
  • DOI: 10.1214/18-ecp191
  • NAID: 120006644043
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] On the Green-Kubo formula and the gradient condition on currents (2018)
  • Author(s): M. Sasada
  • Journal Title: The Annals of Applied Probability Volume: 28 Pages: 2727-2739
  • DOI: 10.1214/17-aap1369
  • Peer Reviewed
• [Journal Article] Thermal Conductivity for Coupled Charged Harmonic Oscillators with Noise in a Magnetic Field (2018)
  • Author(s): K. Sato, M. Sasada
  • Journal Title: Commun. Math. Phys. Volume: 361 Pages: 951-995
  • DOI: 10.1007/s00220-018-3198-5
  • Peer Reviewed
• [Presentation] Stochastic PDE approach to random interfaces (2021)
  • Author(s): 舟木直久
  • Organizer: 信州大学理学部
  • Invited
• [Presentation] Dynamical universality for random matrices and uniqueness of solution of ISDE (2021)
  • Author(s): 長田博文
  • Organizer: Workshop on "Random matrices, Determinantal point processes and Gaussian analytic functions"
  • Int'l Joint Research / Invited
• [Presentation] Biased random walk conditioned on survival among Bernoulli obstacles: subcritical phase (2021)
  • Author(s): 福島竜輝
  • Organizer: 日本数学会年会，慶應義塾大
• [Presentation] Geometry of the random walk range conditioned on survival among Bernoulli obstacles (2021)
  • Author(s): 福島竜輝
  • Organizer: 日本数学会年会，慶應義塾大
• [Presentation] Quenched tail estimate for the random walk in random scenery II (2021)
  • Author(s): 福島竜輝
  • Organizer: 日本数学会年会，慶應義塾大
• [Presentation] Pitman's transform description and invariant measures for KdV- and Toda-type discrete locally-defined dynamics (2021)
  • Author(s): 佐々田槙子
  • Organizer: Mathematical physics and probability joint online seminar at University of Arizona and University of Utah
  • Int'l Joint Research / Invited
• [Presentation] Motion by mean curvature and coupled KPZ from particle systems (2020)
  • Author(s): 舟木直久
  • Organizer: Asia-Pacific Analysis and PDE Seminar, University of Sydney Zoom Webinar
  • Int'l Joint Research / Invited
• [Presentation] Derivation of coupled KPZ equation from multi-species zero-range processes (2020)
  • Author(s): 舟木直久
  • Organizer: Webinar on Stochastic Analysis, 中国科学院・北京理工大学
  • Int'l Joint Research / Invited
• [Presentation] KPZ limit for interacting particle systems (2020)
  • Author(s): 舟木直久
  • Organizer: Yau Mathematical Sciences Center, 清華大学
  • Int'l Joint Research / Invited
• [Presentation] Quasilinear stochastic PDE and its asymptotics in noise (2020)
  • Author(s): 舟木直久
  • Organizer: International Workshop on Multiphase Flows: Analysis, Modelling and Numerics, Oxford-Waseda in Mathetatics
  • Int'l Joint Research / Invited
• [Presentation] Spin current statistics for the quantum 1D XX spin chain and the Bessel kernel (2020)
  • Author(s): 笹本智弘
  • Organizer: CMI-HIMR Integrable Probability Summer School
  • Int'l Joint Research / Invited
• [Presentation] Current moment formulas for 1D exclusion processes (2020)
  • Author(s): 笹本智弘
  • Organizer: New Connections in Integrable Systems
  • Int'l Joint Research / Invited
• [Presentation] Geometric Perspective for the Theory of Hydrodynamic Limits (2020)
  • Author(s): 佐々田槙子
  • Organizer: iTHEMS math-phys joint seminar
  • Int'l Joint Research / Invited
• [Presentation] Hydrodynamic limit of nongradient models (2020)
  • Author(s): 佐々田槙子
  • Organizer: One World Probability Seminar
  • Int'l Joint Research / Invited
• [Presentation] Discrete integrable systems and Pitman's transformation (2020)
  • Author(s): 佐々田槙子
  • Organizer: UCLA probability seminar
  • Int'l Joint Research / Invited
• [Presentation] Geometric Perspectives for the Theory of Hydrodynamic Limits (2020)
  • Author(s): 佐々田槙子
  • Organizer: Department Colloquium at McMaster University
  • Int'l Joint Research / Invited
• [Presentation] 流体力学極限の幾何学的考察 (Part 1) (2020)
  • Author(s): 佐々田槙子
  • Organizer: 代数的整数論とその周辺
  • Invited
• [Presentation] General solutions and invariant measures for systems of KdV- and Toda-type locally-defined dynamics (2020)
  • Author(s): 佐々田槙子
  • Organizer: Cornell probability seminar
  • Int'l Joint Research / Invited
• [Presentation] General solutions and invariant measures for systems of KdV- and Toda-type locally-defined dynamics (2020)
  • Author(s): 佐々田槙子
  • Organizer: Kansai Probability Seminar
  • Invited
• [Presentation] 非勾配型モデルに対する流体力学極限の幾何学的考察 (2020)
  • Author(s): 佐々田槙子
  • Organizer: 確率論シンポジウム
• [Presentation] Biased random walk conditioned on survival among Bernoulli obstacles: sub-critical phase (2020)
  • Author(s): 福島竜輝
  • Organizer: Spectra of Random Operators and Related Topics，学習院大学
  • Int'l Joint Research / Invited
• [Presentation] Sharp interface limit for stochastic Allen-Cahn equations (2019)
  • Author(s): 舟木直久
  • Organizer: 2019 Spring Probability Workshop, 中央研究院数学研究所, 台北, 台湾
  • Int'l Joint Research / Invited
• [Presentation] Three different time stages in stochastic mass-conserving Allen-Cahn equation (2019)
  • Author(s): 舟木直久
  • Organizer: Recent Trends in Stochastic Analysis and SPDEs, University of Pisa, Italy
  • Int'l Joint Research / Invited
• [Presentation] Large deviation for lozenge tiling dynamics (2019)
  • Author(s): 舟木直久
  • Organizer: 第12回日本数学会季期研究所: Stochastic Analysis, Random Fields and Integrable Probability, 九州大学
  • Int'l Joint Research / Invited
• [Presentation] Scaling limits for random fields in two media (2019)
  • Author(s): 舟木直久
  • Organizer: Gradient Flows and Related Topics: Analysis and Applications, 石川県政記念しいのき迎賓館
  • Invited
• [Presentation] Mean curvature interface limit from Glauber-Zero range interacting particles (2019)
  • Author(s): 舟木直久
  • Organizer: Japanese-German Open Conference on Stochastic Analysis 2019, 福岡大学
  • Int'l Joint Research / Invited
• [Presentation] Stochastic mass-conserving Allen-Cahn equation (2019)
  • Author(s): 舟木直久
  • Organizer: Seminaire-Groupe de Travail, Probabilites - Statistiques - Controle, ENSTA ParisTech, France
  • Invited
• [Presentation] Large deviation for lozenge tiling dynamics (2019)
  • Author(s): 舟木直久
  • Organizer: Oberwolfach Workshop Large Scale Stochastic Dynamics, Mathematisches Forschungsinstitut Oberwolfach, Germany
  • Int'l Joint Research / Invited
• [Presentation] Motion by mean curvature and coupled KPZ from particle systems (2019)
  • Author(s): 舟木直久
  • Organizer: Mathematical Analysis for Biology and Ecology, ReaDiNet Conference, Nancy, France
  • Int'l Joint Research / Invited
• [Presentation] Derivation of coupled KPZ equation from multi-species zero-range processes (2019)
  • Author(s): 舟木直久
  • Organizer: 18th Stochastic Analysis on Large Scale Interacting Systems, 大阪大学
• [Presentation] Diffusion in Coulomb environment and a phase transition (2019)
  • Author(s): 長田博文
  • Organizer: Workshop on Probabilistic Methods in Statistical Mechanics of Random Media and Random Fields, Leiden University, Netherlands
  • Int'l Joint Research / Invited
• [Presentation] Diffusion in Coulomb environment and a phase transition (2019)
  • Author(s): 長田博文
  • Organizer: RIMS共同研究(公開型)「量子場の数理とその周辺 2019」京都大学数理解析研究所
  • Invited
• [Presentation] Random matrices and dynamics of infinite particle systems (2019)
  • Author(s): 長田博文
  • Organizer: Interactions between commutative and non-commutative probability, 京都大学
  • Int'l Joint Research / Invited
• [Presentation] Diffusion in Coulomb environment and a phase transition (2019)
  • Author(s): 長田博文
  • Organizer: Japanese-German Open Conference on Stochastic Analysis 2019, 福岡大学
  • Int'l Joint Research / Invited
• [Presentation] Infinite-dimensional stochastic differential equation arising from the planner Gaussian analytic function (2019)
  • Author(s): 長田博文
  • Organizer: 18th Stochastic Analysis on Large Scale Interacting Systems, 大阪大学
• [Presentation] Analytic confirmation of a nonlinear fluctuating hydrodynamics prediction for a two species asymmetric exclusion process (2019)
  • Author(s): 笹本智弘
  • Organizer: Emergent Hydrodynamics In Low Dimensional Quantum Systems, Natal, Brazil
  • Int'l Joint Research / Invited
• [Presentation] Exact confirmation of the nonlinear fluctuating hydrodynamics for a two species asymmetric exclusion process (2019)
  • Author(s): 笹本智弘
  • Organizer: STATPHYS27, Buenos Aires, Argentina
  • Int'l Joint Research
• [Presentation] Large deviation of spin current for the 1D XX spin chain with domain wall boundary condition (2019)
  • Author(s): 笹本智弘
  • Organizer: Classical and Quantum Integrable Systems 2019, St. Petersburg, Russia
  • Int'l Joint Research / Invited
• [Presentation] Spin current for the quantum 1D XX spin chain and the Bessel kernel (2019)
  • Author(s): 笹本智弘
  • Organizer: Interactions between commutative and non-commutative probability, 京都大学
  • Int'l Joint Research / Invited
• [Presentation] Spin current for the quantum 1D XX spin chain and the Bessel kernel (2019)
  • Author(s): 笹本智弘
  • Organizer: School and Workshop on Random Matrix Theory and Point Processes, Trieste, Italy
  • Int'l Joint Research / Invited
• [Presentation] Large deviation of spin current for the 1D XX spin chain with domain wall boundary condition (2019)
  • Author(s): 笹本智弘
  • Organizer: Workshop on Recent Progress in Mathematical and Statistical Physics, 東京
  • Int'l Joint Research / Invited
• [Presentation] On the random matrix type multiple contour integrals for particle systems (2019)
  • Author(s): 笹本智弘
  • Organizer: Spectra of Random Operators and Related Topics, 学習院大学
  • Int'l Joint Research / Invited
• [Presentation] Fluctuations for a two species asymmetric exclusion process (2019)
  • Author(s): 笹本智弘
  • Organizer: 18th Stochastic Analysis on Large Scale Interacting Systems, 大阪大学
  • Invited
• [Presentation] Large deviations for 1D exclusion process (2019)
  • Author(s): 笹本智弘
  • Organizer: Stochastic Analysis on Particle Systems, 横浜
  • Invited
• [Presentation] Annealed random walk among Bernoulli obstacles (2019)
  • Author(s): 福島竜輝
  • Organizer: Japan-Netherlands workshop on Probabilistic Methods in Statistical Mechanics of Random Media, Lorentz center Leiden, Netherlands
  • Int'l Joint Research / Invited
• [Presentation] Zero temperature limit for directed polymers in random environment (2019)
  • Author(s): 福島竜輝
  • Organizer: 第12回日本数学会季期研究所: Stochastic Analysis, Random Fields and Integrable Probability, 九州大学
  • Int'l Joint Research / Invited
• [Presentation] Tail estimates for random walk in random scenery (2019)
  • Author(s): 福島竜輝
  • Organizer: Japanese-German Open Conference on Stochastic Analysis 2019, 福岡大学
  • Int'l Joint Research / Invited
• [Presentation] Random walks among Bernoulli obstacles (2019)
  • Author(s): 福島竜輝
  • Organizer: CIRM Workshop Self-interacting Random Walks, Polymers and Folding，CIRM Marseille, France
  • Int'l Joint Research / Invited
• [Presentation] Biased random walk conditioned on survival among Bernoulli obstacles: sub-critical phase (2019)
  • Author(s): 福島竜輝
  • Organizer: RIMS Workshop Rigorous statistical mechanics and related topics, 京都大学
  • Int'l Joint Research / Invited
• [Presentation] Random walk conditioned on survival among Bernoulli obstacles (2019)
  • Author(s): 福島竜輝
  • Organizer: 台湾数学会年会，National Chung Hsing University, 台湾
  • Int'l Joint Research / Invited
• [Presentation] Biased random walk conditioned on survival among Bernoulli obstacles: sub-critical phase (2019)
  • Author(s): 福島竜輝
  • Organizer: 確率論シンホジウム，慶應大学
• [Presentation] Generalized Pitman's Transform and Discrete Integrable Systems (2019)
  • Author(s): 佐々田槙子
  • Organizer: 第12回日本数学会季期研究所: Stochastic Analysis, Random Fields and Integrable Probability, 九州大学
  • Int'l Joint Research / Invited
• [Presentation] The Box-ball System, Discrete Integrable Systems and Generalized Pitman's Transform (2019)
  • Author(s): 佐々田槙子
  • Organizer: Fall 2019 Minerva Lectures、Columbia University, U.S.A.
  • Invited
• [Presentation] Discrete classical integrable systems and generalized Pitman's transform (2019)
  • Author(s): 佐々田槙子
  • Organizer: Oberwolfach Workshop Large Scale Stochastic Dynamics, Mathematisches Forschungsinstitut Oberwolfach, Germany
  • Int'l Joint Research / Invited
• [Presentation] The macroscopic diffusion coefficient and the gradient condition on microscopic currents (2019)
  • Author(s): 佐々田槙子
  • Organizer: Particle Systems and PDE's VIII, the University of Lisbon, Portugal
  • Int'l Joint Research / Invited
• [Presentation] Hydrodynamic limits for stochastic systems (2019)
  • Author(s): 舟木直久
  • Organizer: Gran Sasso Science Institute, Series of Lectures, イタリア L'Aquila
  • Invited
• [Presentation] Stochastic PDE approach to random interfaces (2019)
  • Author(s): 舟木直久
  • Organizer: Spring School on Random Interfaces Pisa-Augsburg School, Series of Lectures, Augsburg大学, ドイツ
  • Invited
• [Presentation] Derivation of coupled KPZ-Burgers equation from multi-species zero-range processes (2019)
  • Author(s): 舟木直久
  • Organizer: New Directions in Stochastic Analysis: Rough Paths, SPDEs and Related Topics, ツーゼ研究所ベルリン
  • Int'l Joint Research / Invited
• [Presentation] A scheme solving infinite-dimensional stochastic differential equations (2019)
  • Author(s): 長田博文
  • Organizer: Workshop on Random matrices, stochastic geometry, and related topics, シンガポール国立大学
  • Int'l Joint Research / Invited
• [Presentation] Large deviation of spin current for the 1D XX spin chain (2019)
  • Author(s): 笹本智弘
  • Organizer: Spectra of Random Operators and Related Topics, 京都
  • Invited
• [Presentation] KPZ fluctuations for a two species asymmetric exclusion process (2019)
  • Author(s): 笹本智弘
  • Organizer: Rikko MathPhys 2019, 東京
  • Invited
• [Presentation] Geometry of the random walk conditioned to survive among Bernoulli obstacles (2019)
  • Author(s): 福島竜輝
  • Organizer: Spectra of Random Operators and Related Topics, 京都大学
  • Int'l Joint Research / Invited
• [Presentation] Much ado about random walk range (2019)
  • Author(s): 福島竜輝
  • Organizer: Second meeting for GlobalMathNetwork, 京都大学
  • Int'l Joint Research / Invited
• [Presentation] Geometry of the random walk conditioned to survive among Bernoulli obstacles (2019)
  • Author(s): 福島竜輝
  • Organizer: Stochastic Processes and Related Topics, 関西大学
  • Int'l Joint Research / Invited
• [Presentation] ミクロな世界とマクロな世界 (2019)
  • Author(s): 佐々田槙子
  • Organizer: 第９回山田研究会「第２回 自然科学の数学的原理」、京都大学
  • Invited
• [Presentation] 一般化 Pitman 変換と離散可積分系 (2019)
  • Author(s): 佐々田槙子
  • Organizer: 慶應確率論ワークショップ2019、慶應義塾大学日吉キャンパス
  • Invited
• [Presentation] Derivation of coupled KPZ equation from multi-color zero-range processes (2018)
  • Author(s): 舟木直久
  • Organizer: ニューヨーク大学上海校
  • Invited
• [Presentation] Motion by mean curvature from Glauber-Kawasaki dynamics (2018)
  • Author(s): 舟木直久
  • Organizer: Interplay of Random Media and Stochastic Interface Models， Berlin工科大学
  • Int'l Joint Research / Invited
• [Presentation] Coupled KPZ (Kardar-Parisi-Zhang) equation (2018)
  • Author(s): 舟木直久
  • Organizer: The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, 国立台湾大学
  • Int'l Joint Research / Invited
• [Presentation] Motion by mean curvature from Glauber-Kawasaki dynamics (2018)
  • Author(s): 舟木直久
  • Organizer: The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, 国立台湾大学
  • Int'l Joint Research / Invited
• [Presentation] Derivation of coupled KPZ equation from multi-color zero-range process (2018)
  • Author(s): 舟木直久
  • Organizer: Stochastic partial differential equations and related topics, 信州大学理学部
  • Invited
• [Presentation] Hydrodynamic limit for exclusion processes (2018)
  • Author(s): 舟木直久
  • Organizer: KAIST Summer School in Probability 2018, Series of Lectures, 韓国 大田
  • Invited
• [Presentation] Coupled KPZ equation (2018)
  • Author(s): 舟木直久
  • Organizer: 2018 Probability Workshop in Gyeongju, 韓国 慶州
  • Int'l Joint Research / Invited
• [Presentation] Derivation of motion by mean curvature and Stefan problem from particle systems (2018)
  • Author(s): 舟木直久
  • Organizer: ReaDiNet 2018 Recent Progresses in Mathematical Theories for Biological Phenomena, 韓国 済州島
  • Int'l Joint Research / Invited
• [Presentation] Derivations of motion by mean curvature and Stefan problem from Glauber-Kawasaki dynamics (2018)
  • Author(s): 舟木直久
  • Organizer: 17th Stochastic Analysis on Large Scale Interacting Systems, 京都大学数理解析研究所
  • Int'l Joint Research
• [Presentation] Diffusion in Coulomb environment and a phase transition (2018)
  • Author(s): 長田博文
  • Organizer: The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, 国立台湾大学
  • Int'l Joint Research / Invited
• [Presentation] Infinite-dimensional stochastic differential equation with symmetry (2018)
  • Author(s): 長田博文
  • Organizer: International Program on Regularity Structures and Stochastic Systems, 中国科学院数学与系統科学研究院, 中国
  • Int'l Joint Research / Invited
• [Presentation] Dynamical universality for random matrices (2018)
  • Author(s): 長田博文
  • Organizer: 9th International Conference on Stochastic Analysis and its Applications, Bielefeld大学
  • Int'l Joint Research / Invited
• [Presentation] 無限粒子系の確率解析学 -古典的確率解析の新展開とランダム行列の力学的普遍性- (2018)
  • Author(s): 長田博文
  • Organizer: 2018年度 日本数学会 秋季総合分科会, 2018年度日本数学会賞秋季賞受賞講演
  • Invited
• [Presentation] IFC condition for infinite-dimensional stochastic differential equations (2018)
  • Author(s): 長田博文
  • Organizer: 17th Stochastic Analysis on Large Scale Interacting Systems, 京都大学数理解析研究所
  • Int'l Joint Research
• [Presentation] Fluctuations of stationary KPZ models and multiple integral (2018)
  • Author(s): 笹本智弘
  • Organizer: Random matrices and their applications, 京都
  • Int'l Joint Research / Invited
• [Presentation] KPZ fluctuations for one-dimensional two species exclusion process (2018)
  • Author(s): 笹本智弘
  • Organizer: International Workshop on Classical and Quantum Integrable Systems, Protvino (Russia)
  • Int'l Joint Research / Invited
• [Presentation] Large deviation of a tagged particle in 1D symmetric exclusion process (2018)
  • Author(s): 笹本智弘
  • Organizer: 19th International Congress in Mathematical Physics, Montreal
  • Int'l Joint Research
• [Presentation] Fluctuations of the stochastic higher spin six vertex model (2018)
  • Author(s): 笹本智弘
  • Organizer: Gaussian Free Fields and Related Topics, 京都
  • Int'l Joint Research / Invited
• [Presentation] Discrete KPZ models and Frobenius determinant (2018)
  • Author(s): 笹本智弘
  • Organizer: Symmetries and Integrability of Difference Equations, 福岡
  • Int'l Joint Research / Invited
• [Presentation] 1次元非平衡多体系におけるKPZ揺らぎ (2018)
  • Author(s): 笹本智弘
  • Organizer: 乱流と遷移：構造、多重スケール、モデル, 京都
  • Int'l Joint Research / Invited
• [Presentation] １次元揺らぐ流体力学における熱モードのより直接的な解析 (2018)
  • Author(s): 笹本智弘, 藤平悠太
  • Organizer: 京田辺
• [Presentation] Geometry of the random walk conditioned to survive among Bernoulli obstacles (2018)
  • Author(s): 福島竜輝
  • Organizer: Interplay of Random Media and Stochastic Interface Models, Berlin工科大学
  • Int'l Joint Research / Invited
• [Presentation] Zero temperature limit for Brownian directed polymer in Poissonian disasters (2018)
  • Author(s): 福島竜輝
  • Organizer: 9th International Conference on Stochastic Analysis and its Applications, Bielefeld大学
  • Int'l Joint Research / Invited
• [Presentation] Tail estimates for random walk in random scenery (2018)
  • Author(s): 福島竜輝
  • Organizer: Gaussian free fields and related topics, 京都大学
  • Int'l Joint Research / Invited
• [Presentation] Geometry of the random walk conditioned to survive among Bernoulli obstacles (2018)
  • Author(s): 福島竜輝
  • Organizer: 確率論シンポジウム, 京都大学
• [Presentation] On the Green-Kubo Formula and the Gradient Condition on Currents (2018)
  • Author(s): 佐々田槙子
  • Organizer: The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications、国立台湾大学
  • Int'l Joint Research / Invited
• [Presentation] Dynamics of the box-ball system with random initial conditions via Pitman's transformation (2018)
  • Author(s): 佐々田槙子
  • Organizer: XIX International Congress on Mathematical Physics、Centre Mont-Royal, カナダ
  • Int'l Joint Research / Invited
• [Presentation] Dynamics of the box-ball system with random initial conditions via Pitman's transformation (2018)
  • Author(s): 佐々田槙子
  • Organizer: NYU-Shanghai - Kyoto University Young Probabilists' Meeting、NYU-Shanghai, 中国
  • Int'l Joint Research / Invited
• [Presentation] HYDRODYNAMIC LIMIT FOR DEGENERATE DYNAMICS (2018)
  • Author(s): 佐々田槙子
  • Organizer: 17th Stochastic Analysis on Large Scale Interacting Systems、京都大学
  • Int'l Joint Research / Invited
• [Presentation] Dynamics of the box-ball system with random initial conditions via Pitman's transformation (2018)
  • Author(s): 佐々田槙子
  • Organizer: SIDE13、JR HAKATA CITY・福岡
  • Int'l Joint Research / Invited
• [Presentation] Some generalization of Pitman’s transform and invariant measures for discrete integrable systems (2018)
  • Author(s): 佐々田槙子
  • Organizer: Scaling limits & SPDEs: recent developments and future directions、Issac Newton Institute for Mathematical Sciences, イギリス
  • Int'l Joint Research / Invited
• [Book] 確率偏微分方程式 (2019)
  • Author(s): 舟木 直久、乙部 厳己、謝 賓
  • Total Pages: 350
  • Publisher: 岩波書店
  • ISBN: 9784000298254
• [Funded Workshop] 18th workshop on Stochastic Analysis on Large Scale Interacting Systems (第18回「大規模相互作用系の確率解析」), 大阪大学 (2019)
• [Funded Workshop] One-day Symposium: Hydrodynamic limit and related topics, 早稲田大学 (2019)
• [Funded Workshop] 17th Stochastic Analysis on Large Scale Interacting Systems, 京都大学数理解析研究所 (2018)