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stochastic evolutions in random environment and their phase transition

Research Project

Project/Area Number 25400136
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

Yoshida Nobuo  名古屋大学, 多元数理科学研究科, 教授 (40240303)

Project Period (FY) 2013-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywordsランダム環境 / ランダム媒質 / 確率成長 / 生存確率 / 零温度極限 / directed polymer / random environment
Outline of Final Research Achievements

We considered the Brownian directed polymers in Poisson environment and invesigated the free energy at zero-temperature. The quantity of interest is the logarithm of the survival probability. However this quantity is not integrable at zero-temperature and classical methods like sub-additive ergodic theorem
are not applicable. To overcome this difficulty, we investigated various new approaches.

Report

(5 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (5 results)

All 2016 2015 2014 2013

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

  • [Journal Article] Limiting Results for the Free Energy of Directed Polymers in Random Environment with Unbounded Jumps2015

    • Author(s)
      F. Comets, R. Fukushima, S. Nakajima, N. Yoshida
    • Journal Title

      J. Stat. Phys

      Volume: Volume 161, Issue 3 Issue: 3 Pages: 577-597

    • DOI

      10.1007/s10955-015-1347-1

    • NAID

      120006644059

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Localization Transition for Polymers in Poissonian Medium.2013

    • Author(s)
      Comets, Francis; Yoshida, Nobuo
    • Journal Title

      Commun. Math. Phys.

      Volume: Vol 323, Issue 1

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] Survival rate for a random walks in disatrous environment2016

    • Author(s)
      N. Yoshida
    • Organizer
      Niigata Probability Workshop
    • Place of Presentation
      新潟大学
    • Year and Date
      2016-01-21
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Survival rate for a certain class of random walks in random obstacles2014

    • Author(s)
      吉田伸生
    • Organizer
      (The 13th Workshop pn Stochaastic Analysis on Large Scale
    • Place of Presentation
      東京大学
    • Year and Date
      2014-11-05 – 2014-11-07
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Survival in desastrous environment2013

    • Author(s)
      Yoshida, Nobuo
    • Organizer
      クレスト報告会
    • Place of Presentation
      東北大学
    • Related Report
      2013 Research-status Report
    • Invited

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Published: 2014-07-25   Modified: 2019-07-29  

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