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Studies on integrable stochastic processes

Research Project

Project/Area Number 16K05192
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionChiba University

Principal Investigator

Imamura Takashi  千葉大学, 大学院理学研究院, 准教授 (70538280)

Project Period (FY) 2016-04-01 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords確率論 / 可積分系 / KPZクラス / 非対称単純排他過程 / 可積分確率 / 排他過程 / 確率過程 / 統計物理学 / マクドナルド多項式 / 行列式点過程 / 非対称排他過程 / 可積分確率過程 / KPZ方程式
Outline of Final Research Achievements

In the two models (q-TASEP, SEP) of interacting stochastic particle systems, we have obtained distribution functions of positions of particular particles utilizing their intebrable structures. In the q-TASEP, we have got an explicit form of the distribution function in the stationary state applying a new technique different from conventional ones. In the SEP, we have obtained exact large deviation functions of the distribution of the particle position, utilizing some recent developments in the integrable probability.

Academic Significance and Societal Importance of the Research Achievements

確率過程の中には様々なモデルがあるが、揺らぎの極限的な振舞いはモデルによらない普遍的なものであることが予想される。しかしその普遍的な構造を抽出することは一般に困難である。本研究は確率過程のモデルの背後に潜む数理構造を利用して、分布関数等を厳密に導出することによって、そのような普遍的な極限分布を具体的に知ろうとするものであり、いくつかのモデルでそれを行うことが出来た。本研究によって、普遍的であると予想られる極限分布の構造が明確になった。

Report

(5 results)
  • 2019 Annual Research Report   Final Research Report ( PDF )
  • 2018 Research-status Report
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (18 results)

All 2020 2019 2018 2017 2016 Other

All Int'l Joint Research (2 results) Journal Article (5 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 5 results,  Open Access: 4 results,  Acknowledgement Compliant: 1 results) Presentation (11 results) (of which Int'l Joint Research: 5 results,  Invited: 9 results)

  • [Int'l Joint Research] Saclay研究所(フランス)

    • Related Report
      2017 Research-status Report
  • [Int'l Joint Research]

    • Related Report
      2017 Research-status Report
  • [Journal Article] Stationary Higher Spin Six Vertex Model and q-Whittaker measure2020

    • Author(s)
      Takashi Imamura, Matteo Mucciconi, Tomohiro Sasamoto
    • Journal Title

      Prob. Th. Rel. Fields

      Volume: -- Issue: 3-4 Pages: 923-1042

    • DOI

      10.1007/s00440-020-00966-x

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The q-TASEP with a Random Initial Condition2019

    • Author(s)
      Takashi Imamura and Tomohiro Sasamoto
    • Journal Title

      Theoretical and Mathematical Physics

      Volume: 198 Issue: 1 Pages: 69-88

    • DOI

      10.1134/s0040577919010057

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Fluctuations for stationary q-TASEP2018

    • Author(s)
      Takashi Imamura and Tomohiro Sasamoto
    • Journal Title

      Probability Theory and Related Fields

      Volume: online first Issue: 1-2 Pages: 1-84

    • DOI

      10.1007/s00440-018-0868-3

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Free energy distribution of the stationary O'Connell-Yor directed random polymer model2017

    • Author(s)
      Takashi Imamura, Tomohiro Sasamoto
    • Journal Title

      J. Phys. A

      Volume: 50 Issue: 28 Pages: 285203-285203

    • DOI

      10.1088/1751-8121/aa6e17

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Large deviations of a tracer in the symmetric exclusion process2017

    • Author(s)
      Takashi Imamura, Kirone Mallick, Tomohiro Sasamoto
    • Journal Title

      Physical Review Letters

      Volume: 118 Issue: 16 Pages: 160601-160601

    • DOI

      10.1103/physrevlett.118.160601

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Presentation] Determinantal Structures in the q-Whittaker Measure2019

    • Author(s)
      Takashi Imamura
    • Organizer
      The 12th Mathematical Society of Japan, Seasonal Institute (MSJ-SI) Stochastic Analysis, Random Fields and Integrable Probability
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] q-TASEP, stochastic vertex models and the q-Whittaker measures2019

    • Author(s)
      Takashi Imamura
    • Organizer
      Rigorous Statistical Mechanics and Related Topics
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] q-Whittaker measures and the Schur measures2019

    • Author(s)
      Takashi Imamura
    • Organizer
      Spectra of Random Operators and Related Topics
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] q-Whittaker measures and the Schur measures2018

    • Author(s)
      Takashi Imamura
    • Organizer
      17th International Symposium Stochastic Analysis on Large Scale Interacting Systems
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Fluctuations for stationary q-totally asymmetric simple exclusion process2017

    • Author(s)
      Takashi Imamura
    • Organizer
      SPA2017
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Determinantal structures in the q-Whittaker process2017

    • Author(s)
      Takashi Imamura
    • Organizer
      Infinite Analysis 17
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] q-Whittaker measures and Schur measures2017

    • Author(s)
      今村 卓史
    • Organizer
      Random matrices, determinantal processes and their related topics
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] Fluctuation properties of the stationary q-totally asymmetric simple exclusion process II2017

    • Author(s)
      今村卓史
    • Organizer
      Physical and mathematical approaches to interacting particle systems  -In honor of 70th birthday of Herbert Spohn-
    • Place of Presentation
      東京工業大学大岡山西9号館(東京都・目黒区)
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] q-Whittaker 関数に関連する可積分確率過程における 行列式構造2017

    • Author(s)
      今村卓史
    • Organizer
      日本物理学会第72回年次大会
    • Place of Presentation
      大阪大学豊中キャンパス(大阪府・吹田市)
    • Related Report
      2016 Research-status Report
  • [Presentation] ランダムな初期配置におけるq-TASEPのゆらぎ2016

    • Author(s)
      今村卓史
    • Organizer
      日本物理学会2016年秋季大会
    • Place of Presentation
      金沢大学角間キャンパス(石川県・金沢市)
    • Related Report
      2016 Research-status Report
  • [Presentation] q-Whittaker過程における行列式構造2016

    • Author(s)
      今村卓史
    • Organizer
      ランダム作用素のスペクトルと関連する話題
    • Place of Presentation
      慶応大学日吉キャンパス来往舎2階中会議室(神奈川県・横浜市)
    • Related Report
      2016 Research-status Report
    • Invited

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Published: 2016-04-21   Modified: 2021-02-19  

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