Phase transition in stochastic models and its analysis near critical point

2013 Fiscal Year Final Research Report

• Project/Area Number: 24840007
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: University of Tsukuba
• Principal Investigator: NAKASHIMA Makoto 筑波大学, 数理物質系, 助教 (60635902)
• Project Period (FY): 2012-08-31 – 2014-03-31
• Keywords: 確率熱方程式 / 一意性 / 測度値確率過程 / ディレクティドポリマー / ランダム媒質

Research Abstract

We constructed super-Brownian motion in random environment from ``critical" branching random walks in random environment. We characterized this process as a solution to some stochastic heat equation. Moreover, we proved the weak uniquenss of non-negative solutions to the SPDE.

Research Products

• [Presentation] ランダム環境中の分枝ランダムウォークと双対過程 (2013)
  • Author(s): 中島誠
  • Organizer: 新潟確率論ワークショップ
  • Place of Presentation: 新潟大学
  • Year and Date: 2013-12-05
• [Presentation] Branching random walks in random environment (2013)
  • Author(s): 中島誠
  • Organizer: 2013年度日本数学会秋季分科会
  • Place of Presentation: 愛媛大学
  • Year and Date: 2013-09-24
• [Presentation] Branching random walks in random environment and super-Brownian motion in random environment (2013)
  • Author(s): 中島誠
  • Organizer: Applications of RG methods in Mathematical Sciences
  • Place of Presentation: 数理解析研究所 (京都大学)
  • Year and Date: 2013-09-11
• [Presentation] Super-Brownian motion in random environment arising from branching random walks in random environment (2013)
  • Author(s): 中島誠
  • Organizer: The 2^<nd> workshop on Universality and Scaling Limits in Probability and Statistical Mechanics
  • Place of Presentation: 北海道大学
  • Year and Date: 2013-08-06
• [Presentation] ランダム環境中のスーパーブラウン運動 (2013)
  • Author(s): 中島誠
  • Organizer: 2013年度日本数学会年会
  • Place of Presentation: 京都大学
  • Year and Date: 2013-03-20
• [Presentation] ランダム環境中の分枝ランダムウォークと測度値確率過程 (2012)
  • Author(s): 中島誠
  • Organizer: 確率論シンポジウム
  • Place of Presentation: 京都大学
  • Year and Date: 2012-12-20
• [Presentation] Super-Brownian motion in random environment and heat equation with noise (2012)
  • Author(s): 中島誠
  • Organizer: Stochastic Analysis and Applications
  • Place of Presentation: 岡山大学
  • Year and Date: 2012-09-28
• [Book] 確率論ハンドブック (2012)
  • Author(s): 渡辺信三, 重川一郎 (他, 中島誠)
  • Total Pages: 422-423
  • Publisher: 丸善出版