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2016 Fiscal Year Annual Research Report

Stochastic processes on disordered media -- discrete models and their scaling limits

Research Project

Project/Area Number 25247007
Research InstitutionKyoto University

Principal Investigator

熊谷 隆  京都大学, 数理解析研究所, 教授 (90234509)

Co-Investigator(Kenkyū-buntansha) 相川 弘明  北海道大学, 理学研究院, 教授 (20137889)
竹田 雅好  東北大学, 理学研究科, 教授 (30179650)
日野 正訓  京都大学, 情報学研究科, 准教授 (40303888)
舟木 直久  東京大学, 大学院数理科学研究科, 教授 (60112174)
木上 淳  京都大学, 情報学研究科, 教授 (90202035)
Project Period (FY) 2013-04-01 – 2017-03-31
Keywords確率論 / 数理物理 / 解析学 / 複雑系 / 統計力学 / 熱方程式
Outline of Annual Research Achievements

1。熊谷は、一般の距離付き測度空間における飛躍型確率過程に関する楕円型ハルナック不等式及び放物型ハルナック不等式の同値条件を研究し、これらの不等式の安定性を証明した。(Z.Q. Chen氏、J. Wang氏との共同研究で、前者は論文が雑誌掲載予定、後者は論文を投稿中。)木上は、Stretched Sierpinski gasketと呼ばれるSierpinski gasketの分岐点を区間で置き換えた集合上の確率過程の研究を行い、symmetricなlocal regular Dirichlet formの完全な分類を行った。
2。相川は、非有界集合の容量密度について考察した。半径一定の球に対する容量密度の中心を動かしたときの下限(下容量密度)を研究し、半径を大きくしたときの下容量密度の極限値は0か1に限る0-1法則(dichotomy)を様々な状況で示した。また、竹田は既約性, 強フェラー性, 緊密性なる三つの性質をもつ対称マルコフ過程の半群はコンパクト作用素になることを示し、時間変更過程や吸収壁マルコフ過程の半群やファインマン・カッツ半群のなかに応用例を見つけた。
3。舟木は、発散項を持つ確率偏微分方程式である KPZ 方程式、多成分 KPZ 方程式、質量保存確率アレン・カーン方程式の鋭敏界面極限、確率的摂動を持つ平均曲率運動、数理生物で用いられるAdaptive dynamicsの基礎付け、1階の確率偏微分方程式の離散近似などについて考察した。
4。日野は、一般の状態空間において強局所ディリクレ形式に低階項の摂動を加えた2次形式に付随する正値保存半群の短時間漸近評価について研究し、半群が積分型ヴァラダン評価を持つための十分条件を与えた。

Research Progress Status

28年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

28年度が最終年度であるため、記入しない。

  • Research Products

    (31 results)

All 2018 2017 2016 Other

All Int'l Joint Research (5 results) Journal Article (9 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 8 results,  Open Access: 1 results) Presentation (14 results) (of which Int'l Joint Research: 13 results,  Invited: 14 results) Book (1 results) Remarks (1 results) Funded Workshop (1 results)

  • [Int'l Joint Research] University of British Columbia(Canada)

    • Country Name
      Canada
    • Counterpart Institution
      University of British Columbia
  • [Int'l Joint Research] Fujian Normal University(China)

    • Country Name
      China
    • Counterpart Institution
      Fujian Normal University
  • [Int'l Joint Research] Seoul National University(韓国)

    • Country Name
      KOREA (REP. OF KOREA)
    • Counterpart Institution
      Seoul National University
  • [Int'l Joint Research] University of Oxford/University of Warwick(United Kingdom)

    • Country Name
      United Kingdom
    • Counterpart Institution
      University of Oxford/University of Warwick
  • [Int'l Joint Research] Stanford University/University of Washington(米国)

    • Country Name
      U.S.A.
    • Counterpart Institution
      Stanford University/University of Washington
  • [Journal Article] Elliptic Harnack inequalities for symmetric non-local Dirichlet forms.2018

    • Author(s)
      Z.-Q. Chen, T. Kumagai and J. Wang
    • Journal Title

      J. Math. Pures Appl.

      Volume: 掲載予定 Pages: 掲載予定

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Completely symmetric resistance forms on the stretched Sierpinski gasket.2018

    • Author(s)
      P. Alonso Ruiz, U. Freiberg and J. Kigami
    • Journal Title

      Journal of Fractal Geometry

      Volume: 掲載予定 Pages: 掲載予定

    • Peer Reviewed
  • [Journal Article] Time-changes of stochastic processes associated with resistance forms.2017

    • Author(s)
      D.A. Croydon, B.M. Hambly and T. Kumagai
    • Journal Title

      Electron. J. Probab.

      Volume: 22 Pages: 1--41

    • DOI

      10.1214/17-EJP99

    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] A coupled KPZ equation, its two types of approximations and existence of global solutions.2017

    • Author(s)
      T. Funaki and M. Hoshino
    • Journal Title

      Journal of Functional Analysis

      Volume: 273 Pages: 1165~1204

    • DOI

      https://doi.org/10.1016/j.jfa.2017.05.002

    • Peer Reviewed
  • [Journal Article] Compactness of Markov and Schroedinger semi-groups: a probabilistic approach.2017

    • Author(s)
      M. Takeda, Y. Tawara and K. Tsuchida
    • Journal Title

      Osaka J. Math.

      Volume: 54 Pages: 57--532

    • Peer Reviewed
  • [Journal Article] Indices of Dirichlet forms.2017

    • Author(s)
      M. Hino
    • Journal Title

      Sugaku Expositions

      Volume: 30 Pages: 187--205

    • DOI

      https://doi.org/10.1090/suga/423

  • [Journal Article] Laws of the iterated logarithm for random walks on Random Conductance Models.2016

    • Author(s)
      T. Kumagai and C. Nakamura
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: B59 Pages: 141--156

    • Peer Reviewed
  • [Journal Article] Dichotomy of global density of Riesz capacity.2016

    • Author(s)
      H. Aikawa
    • Journal Title

      Studia Math.

      Volume: 232 Pages: 1--12

    • DOI

      10.4064/sm8511-4-2016

    • Peer Reviewed
  • [Journal Article] Large time asymptotics of Feynman-Kac functionals for symmetric stable processes.2016

    • Author(s)
      M. Takeda and M. Wada
    • Journal Title

      Math. Nachr.

      Volume: 289 Pages: 2069--2082

    • DOI

      10.1002/mana.201500136

    • Peer Reviewed
  • [Presentation] Criticality and Subcriticality for Positive Schroedinger Forms2017

    • Author(s)
      M. Takeda
    • Organizer
      Dirichlet forms and their geometry
    • Int'l Joint Research / Invited
  • [Presentation] An integrated version of Varadhan's asymptotics for lower order perturbations of strong local Dirichlet forms2017

    • Author(s)
      M. Hino
    • Organizer
      Dirichlet forms and their geometry
    • Int'l Joint Research / Invited
  • [Presentation] Completely symmetric resistance forms on the stretched Sierpinski gasket2017

    • Author(s)
      J. Kigami
    • Organizer
      Dirichlet forms and their geometry
    • Int'l Joint Research / Invited
  • [Presentation] Stability of heat kernel estimates and parabolic Harnack inequalities for jump processes on metric measure spaces2016

    • Author(s)
      T. Kumagai
    • Organizer
      Stochastic Partial Differential Equations and Related Fields
    • Int'l Joint Research / Invited
  • [Presentation] Time changes of stochastic processes associated with resistance forms2016

    • Author(s)
      T. Kumagai
    • Organizer
      Random Structures in High Dimensions
    • Int'l Joint Research / Invited
  • [Presentation] Lamplighter random walks on fractals2016

    • Author(s)
      T. Kumagai
    • Organizer
      3rd Workshop on Probability Theory and its Applications
    • Int'l Joint Research / Invited
  • [Presentation] 複雑な系の上の異常拡散現象の解析2016

    • Author(s)
      熊谷隆
    • Organizer
      日本数学会秋季総合分科会、企画特別講演
    • Invited
  • [Presentation] Coupled KPZ equation2016

    • Author(s)
      T. Funaki
    • Organizer
      Stochastic Partial Differential Equations and Applications - X"
    • Int'l Joint Research / Invited
  • [Presentation] Sharp interface limit for a stochastically perturbed mass conserving Allen-Cahn equation2016

    • Author(s)
      T. Funaki
    • Organizer
      Stochastic Partial Differential Equations and Related Fields
    • Int'l Joint Research / Invited
  • [Presentation] Coupled KPZ equation2016

    • Author(s)
      T. Funaki
    • Organizer
      Large Scale Stochastic Dynamics
    • Int'l Joint Research / Invited
  • [Presentation] Boundary Harnack Principle and smoothness of the domain2016

    • Author(s)
      H. Aikawa
    • Organizer
      XVIIIth Conference on Analytic Functions and Related Topics
    • Int'l Joint Research / Invited
  • [Presentation] Minimal smoothness for the global boundary Harnack principle2016

    • Author(s)
      H. Aikawa
    • Organizer
      3rd Workshop on Probability Theory and its Applications
    • Int'l Joint Research / Invited
  • [Presentation] Spectral properties of symmetric Markov processes with tightness property2016

    • Author(s)
      M. Takeda
    • Organizer
      Stochastic Partial Differential Equations and Related Fields
    • Int'l Joint Research / Invited
  • [Presentation] Integrated version of Varadhan's asymptotics for first-order perturbations of strong local Dirichlet forms2016

    • Author(s)
      M. Hino
    • Organizer
      The 8th International Conference on Stochastic Analysis and Its Applications
    • Int'l Joint Research / Invited
  • [Book] Lectures on random interfaces2016

    • Author(s)
      T. Funaki
    • Total Pages
      138
    • Publisher
      Springer
    • ISBN
      978-981-10-0849-8
  • [Remarks] Takashi Kumagai's home page

    • URL

      http://www.kurims.kyoto-u.ac.jp/~kumagai/kumpre.html

  • [Funded Workshop] Heat Kernels, Stochastic Processes and Functional Inequalities (Oberwolfach)2016

URL: 

Published: 2018-12-17   Modified: 2022-02-22  

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