Phase transition in stochastic models and its analysis near critical point

• 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
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000); Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• 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 / SPDE / ランダム環境中の分枝ランダムウォーク

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

• [Journal Article] Branching random walks in random environment and Super-Brownian motion in random environment (2014)
  • Author(s): Makoto Nakashima
  • Journal Title: Annales de L'Institut Henri Poincare Volume: 印刷中
  • Peer Reviewed
• [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] Super-Brownian motion in random environment arising from branching random walks in random environemt (2013)
  • Author(s): Makoto Nakashima
  • Organizer: The 2nd workshop on University and Scaling Limits in Probability and Statistical Mechanics
  • Place of Presentation: 北海道大学
  • Invited
• [Presentation] Branching random walks in random environment and super-Brownian motion in random environment (2013)
  • Author(s): Makoto Nakashima
  • Organizer: Applicatios of RG Methods in Mathematical Sciences
  • Place of Presentation: 京都大学 数理解析研究所
  • Invited
• [Presentation] Branching random walks in random environment (2013)
  • Author(s): 中島誠
  • Organizer: 日本数学会2013年度秋季総合分科会
  • Place of Presentation: 愛媛大学
  • Invited
• [Presentation] ランダム環境中の超過程と双対過程 (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
  • Invited
• [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
• [Presentation] Super-Brownian motion in random environment and heat equation with white noise.
  • Author(s): 中島誠
  • Organizer: Stochastic Analysis and Applications
  • Place of Presentation: 岡山大学
• [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
  • Author(s): 中島誠
  • Organizer: 確率論シンポジウム
  • Place of Presentation: 数理解析研究所(京都)
• [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)
  • Publisher: 丸善出版