stochastic evolutions in random environment and their phase transition

• Project/Area Number: 25400136
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Nagoya 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: ¥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.

Research Products

• [Journal Article] Limiting Results for the Free Energy of Directed Polymers in Random Environment with Unbounded Jumps (2015)
  • 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
  • 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
  • Peer Reviewed
• [Presentation] Survival rate for a random walks in disatrous environment (2016)
  • Author(s): N. Yoshida
  • Organizer: Niigata Probability Workshop
  • Place of Presentation: 新潟大学
  • Year and Date: 2016-01-21
  • Int'l Joint Research / Invited
• [Presentation] Survival rate for a certain class of random walks in random obstacles (2014)
  • 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
  • Invited
• [Presentation] Survival in desastrous environment (2013)
  • Author(s): Yoshida, Nobuo
  • Organizer: クレスト報告会
  • Place of Presentation: 東北大学
  • Invited