Phase transitions from the view point of stochastic processes

2008 Fiscal Year Final Research Report

• Project/Area Number: 17540112
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kyoto University
• Principal Investigator: YOSHIDA Nobuo Kyoto University, 大学院・理学研究科, 准教授 (40240303)
• Project Period (FY): 2005 – 2008
• Keywords: random walk / random environment / localization

Research Abstract

媒質からの影響を表すパラメーターβ>0を導入する(統計力学で言う「逆温度に相当」)。このとき、空間1, 2次元では任意のβ>0で高分子の局在が起る。一方 空間 3次元、あるいはそれ以上では、相転移が起る。つまり、ある 臨界値 β_c が存在し、β < β_c では拡散相、β > β_c で局在相となる。

Research Products

• [Journal Article] Central Limit Theorem for a Class ofLinear Systems, Electron (2009)
  • Author(s): Y. Nagahata, N. Yoshida
  • Journal Title: J. Probab
• [Journal Article] Localization for Branching Random Walksin Random Environment, Stoch. Proc (2009)
  • Author(s): Y. Hu, N. Yoshida
  • Journal Title: Appl Vol. 119 Pages: 1632-1651
• [Journal Article] Phase Transitions for the Growth Rate ofLinear Stochastic Evolutions (2008)
  • Author(s): N. Yoshida
  • Journal Title: J. Stat.Phys 13,No.6 Pages: 1033-1058
• [Journal Article] Central Limit Theorem forBranching Random Walk in RandomEnvironment, Ann (2008)
  • Author(s): N. Yoshida
  • Journal Title: Appl. Probab Vol. 18,No. 4 Pages: 1619-1635
• [Journal Article] Directed Polymers inRandom Environment are Diffusive at Weak Disorder (2006)
  • Author(s): F. Comets, N. Yoshida
  • Journal Title: Ann. Probab Vol. 34,No. 5 Pages: 1746-1770
• [Journal Article] Brownian directed polymers in randomenvironment (2005)
  • Author(s): F. Comets, N. Yoshida
  • Journal Title: Commun. Math. Phys 54, no. 2 Pages: 257-287
• [Presentation] Phase Transitions for LinearStochastic Evolutions (2009)
  • Author(s): 吉田伸生
  • Organizer: Random Syetemsand Processes
  • Place of Presentation: 京都大学
  • Year and Date: 2009-02-18
• [Presentation] ランダム行列で記述される粒子系の相転移 (2008)
  • Author(s): 吉田 伸生
  • Organizer: キックオフシンポジウム
  • Place of Presentation: 東北大学
  • Year and Date: 2008-12-26
• [Presentation] ランダム行列で記述される粒子系の相転移 (2008)
  • Author(s): 吉田 伸生
  • Organizer: 確率論シンポジウム
  • Place of Presentation: 東京工業大学
  • Year and Date: 2008-12-26
• [Presentation] Branching Random Walks inRandom Environment (2008)
  • Author(s): 吉田伸生
  • Organizer: Diffusive Behavior andLocalization "Workshop on Random Walks,Particle Systems and Random Media"
  • Place of Presentation: Pontifica UniversidadCatolica de Chile
  • Year and Date: 2008-01-14
• [Presentation] Branching Random Walks inRandom Environment (2007)
  • Author(s): 吉田伸生
  • Organizer: Diffusive Behavior andLocalization 「確率論シンポジウム」
  • Place of Presentation: 熊本大学
  • Year and Date: 2007-12-12
• [Presentation] Diffusive Behavior andLocalization 「確率論シンポジウム」From Parabolic Anderson Modelsto Branching Random Walks in RandomEnvironment (2007)
  • Author(s): 吉田伸生
  • Organizer: Stochastic Problems andNonlinear PDEs
  • Place of Presentation: 京都大学
  • Year and Date: 2007-12-04
• [Presentation] Branching Random Walks inRandom Environment (2007)
  • Author(s): 吉田伸生
  • Organizer: Diffusive Behavior andLocalization "Stochastic analysis of largeinteracting systems
  • Place of Presentation: Nishijin Plaza, Kyusyu University
  • Year and Date: 2007-10-26
• [Presentation] Central limit theorem forbranching random walks in random environment (2007)
  • Author(s): 吉田伸生
  • Organizer: Non-classical interacting random walks
  • Place of Presentation: Oberwolfach
  • Year and Date: 2007-05-22
• [Presentation] Branching random walkrepresentation of directed polymers in randomenvironment (2007)
  • Author(s): 吉田伸生
  • Organizer: 統計物理に関連する数学的話題
  • Place of Presentation: 東京工業大学
  • Year and Date: 2007-01-29
• [Presentation] Directed polymers in randomenvironment (2006)
  • Author(s): 吉田伸生
  • Organizer: EMS MathematicalWeek-End
  • Place of Presentation: UniversiteNantes
  • Year and Date: 2006-06-16
• [Presentation] ランダム媒質中のディレクティドポリマーについて (2006)
  • Author(s): 吉田伸生
  • Organizer: 日本数学会春期学会
  • Place of Presentation: 中央大学
  • Year and Date: 2006-03-26
• [Presentation] Directed polymers in randomenvironment are diffusive at all subcriticaltenperature (2005)
  • Author(s): 吉田伸生
  • Organizer: Some Recent Topics onStochastic Models
  • Place of Presentation: RIMS Kyoto
  • Year and Date: 2005-09-30
• [Presentation] Large time behavior of directedpolymers in random environment (2005)
  • Author(s): 吉田伸生
  • Organizer: 30thStochastic Process and their Applications
  • Place of Presentation: Univ. of California, Santa Barbara
  • Year and Date: 2005-06-27
• [Presentation] Diffusivity of directed polymers inrandom environment (2005)
  • Author(s): 吉田伸生
  • Organizer: The Fifth East AsiaPDE Conference
  • Place of Presentation: Osaka University Nakanoshima Center
  • Year and Date: 2005-01-31
• [Book] ルベール積分入門-使うための理論と演習 (2006)
  • Author(s): 吉田伸生
  • Total Pages: 246
  • Publisher: 遊星社
• [Remarks]
  • URL: http://www.math.kyoto-u.ac.jp/?nobuo/index_j.html