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Dynamics on Random Media

Research Project

Project/Area Number 17F17319
Research Category

Grant-in-Aid for JSPS Fellows

Allocation TypeSingle-year Grants
Section外国
Research Field Basic analysis
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) CAN VAN HAO  京都大学, 数理解析研究所, 外国人特別研究員
CAN HAO  京都大学, 数理解析研究所, 外国人特別研究員
Project Period (FY) 2017-11-10 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 2019: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2018: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2017: ¥400,000 (Direct Cost: ¥400,000)
Keywordsランダムグラフ / イジング模型 / グラウバーダイナミックス / メタスタビリティ
Outline of Annual Research Achievements

昨年度に引き続き、Can氏とインフォーマルなセミナーを行い、さらにメールのやり取り等を通じて以下の研究を行った。
1)正則なランダムグラフ上のグラウバーダイナミックスの混合時間のカットオフ現象について、van der Hofstad教授と3人の共著で以下の論文にまとめ、雑誌に投稿した。Van Hao Can, Remco van der Hofstad, Takashi Kumagai, Glauber dynamics for Ising models on random regular graphs: cut-off and metastability: arXiv:1912.07798
この研究では、低温相(逆温度が大きい場合)で磁場が強ければカットオフ現象が起こり、磁場が弱ければ混合時間が指数増大する(メタスタビリティが起こる)ことを媒質のランダム性について確率1の場合(quenched caseと呼ばれる)と媒質のランダム性についても平均をとる場合(annealed caseと呼ばれる)について示した。さらに、annealed caseではカットオフ現象とメタスタビリティを隔てる臨界磁場が、正則樹木の上のイジング模型の臨界磁場と一致することも示した。
2)定常なランダム媒質中のランダムウォークの熱核評価については、昨年に引き続き媒質の定常性を利用した熱核の下からの対角評価の研究を続けている。媒質に関する仮定が未だにかなりテクニカルな形になっているため、関連するJ.R. Lee氏の論文を詳しく解析することで、より自然な条件にできないかを検討している。また、主結果の応用について、long-range percolation以外の適用例を検討している。本研究については、引き続きCan氏とメール等で連絡を取りながら、共同研究を継続していく予定である。

Research Progress Status

令和元年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

令和元年度が最終年度であるため、記入しない。

Report

(3 results)
  • 2019 Annual Research Report
  • 2018 Annual Research Report
  • 2017 Annual Research Report
  • Research Products

    (19 results)

All 2019 2018 2017 Other

All Int'l Joint Research (3 results) Journal Article (7 results) (of which Int'l Joint Research: 4 results,  Peer Reviewed: 7 results,  Open Access: 2 results) Presentation (8 results) (of which Int'l Joint Research: 6 results,  Invited: 8 results) Remarks (1 results)

  • [Int'l Joint Research] Vietnam Academy of Sci. and Tech.(ベトナム)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] Vietnam Academy of Sci. and Tech.(ベトナム)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Vietnam Academy of Sci. and Tech.(ベトナム)

    • Related Report
      2017 Annual Research Report
  • [Journal Article] Persistence Probability of Random Weyl Polynomial2019

    • Author(s)
      Can Van Hao、Pham Viet-Hung
    • Journal Title

      Journal of Statistical Physics

      Volume: 176 Issue: 1 Pages: 262-277

    • DOI

      10.1007/s10955-019-02298-0

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] First passage time of the frog model has a sublinear variance2019

    • Author(s)
      Can Van Hao、Nakajima Shuta
    • Journal Title

      Electronic Journal of Probability

      Volume: 24 Issue: none Pages: 1-27

    • DOI

      10.1214/19-ejp334

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Persistence probability of a random polynomial arising from evolutionary game theory2019

    • Author(s)
      Can Van Hao、Duong Manh Hong、Pham Viet Viet Hung
    • Journal Title

      Journal of Applied Probability

      Volume: 56 Issue: 3 Pages: 870-890

    • DOI

      10.1017/jpr.2019.50

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Exponential extinction time of the contact process on rank-one inhomogeneous random graphs2019

    • Author(s)
      Van Hao Can
    • Journal Title

      J. Theor. Probab.

      Volume: 32 Issue: 1 Pages: 106-130

    • DOI

      10.1007/s10959-017-0786-9

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Annealed limit theorems for the Ising model on random regular graphs2019

    • Author(s)
      Van Hao Can
    • Journal Title

      Ann. Appl. Probab.

      Volume: 29 Issue: 3 Pages: 1398-1445

    • DOI

      10.1214/17-aap1377

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Mean value inequalities for jump processes2018

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

      Proceedings of Stochastic Partial Differential Equations and Related Fields, In Honor of Michael Roeckner, Springer Proc. in Math and Stat.

      Volume: 229 Pages: 421-437

    • DOI

      10.1007/978-3-319-74929-7_28

    • ISBN
      9783319749280, 9783319749297
    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Super-exponential extinction time of the contact process on random geometric graphs2018

    • Author(s)
      Van Hao Can
    • Journal Title

      Combin. Probab. Comput.

      Volume: 27 Issue: 2 Pages: 162-185

    • DOI

      10.1017/s0963548317000372

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Presentation] The mixing time of the dynamical Ising model on random regular graphs2019

    • Author(s)
      Can Van Hao
    • Organizer
      The 18th Symposium Stochastic Analysis on Large Scale Interacting Systems
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Anomalous random walk and diffusion: from fractals to random media2019

    • Author(s)
      Takashi Kumagai
    • Organizer
      Colloquium at Shanghai JiaoTong University
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] Annealed Ising model on random regular graphs2018

    • Author(s)
      Van Hao Can
    • Organizer
      Mathematical Statistical Mechanics, Random Graphs and Related Topics
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Annealed Ising model on random graphs2018

    • Author(s)
      Van Hao Can
    • Organizer
      NYU Shanghai - Kyoto University Young Probabilists' Meeting
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Sublinearity for the variance of the passage time in frog models2018

    • Author(s)
      Van Hao Can
    • Organizer
      17th International Symposium: Stochastic Analysis on Large Scale Interacting Systems
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Quenched invariance principle for random walks among random conductances with stable-like jumps2018

    • Author(s)
      Takashi Kumagai
    • Organizer
      Non Standard Diffusions in Fluids, Kinetic Equations and Probability at CIRM
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Anomalous random walks on random media2018

    • Author(s)
      Takashi Kumagai
    • Organizer
      Probability Seminar at TU-Berlin
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Annealed Ising model on random regular graphs2017

    • Author(s)
      Van Hao Can
    • Organizer
      Dynamics on random graphs (CIRM, Marseille)
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Remarks] Takashi Kumagai's home page

    • URL

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

    • Related Report
      2019 Annual Research Report 2018 Annual Research Report 2017 Annual Research Report

URL: 

Published: 2017-11-13   Modified: 2024-03-26  

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