Stochastic analysis for the effective interface model

2009 Fiscal Year Final Research Report

• Project/Area Number: 19740058
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Nihon University
• Principal Investigator: NISHIKAWA Takao Nihon University, 理工学部, 講師 (10386005)
• Project Period (FY): 2007 – 2009
• Keywords: 確率論 / 数理物理 / 大規模相互作用系

Research Abstract

The main topic of this research is the analysis for the large scale and long time asymptotic behavior of the effective interface model. First results of this research is the large deviation for the interface model with a conservation law. The next is the characterization for the family of stationary measures for the stochastic dynamics with non-convex potential, and the description of the partial differential equation from scaling limit of the stochastic dynamics.

Research Products

• [Journal Article] Hydrodynamic limit for the interface model with general potentials (2008)
  • Author(s): T. Nishikawa
  • Journal Title: Oberwolfach Report Volume5,Issue4 Pages: 3127-3130
• [Presentation] Hydrodynamic limit for the interface model with general potentials (2009)
  • Author(s): 西川貴雄
  • Organizer: 研究集会「Topics on Random Media」
  • Place of Presentation: 京都大学
  • Year and Date: 2009-09-15
• [Presentation] Hydrodynamic limit for the interface model with general potentials (2008)
  • Author(s): 西川貴雄
  • Organizer: 研究集会「Interplay of Analysis and Probability in Physics」
  • Place of Presentation: Oberwolfach(ドイツ)
  • Year and Date: 2008-12-06
• [Presentation] 一般化されたポテンシャルを持つ界面モデルに対する流体力学極限 (2008)
  • Author(s): 西川貴雄
  • Organizer: 研究集会「大規模相互作用系の確率解析」
  • Place of Presentation: 東京大学
  • Year and Date: 2008-11-04
• [Presentation] Large deviation for the Ginzburg-Landau∇φinterface model with conservation law (2008)
  • Author(s): 西川貴雄
  • Organizer: 研究集会「Workshop on Gradient Models and Elasticity」
  • Place of Presentation: University of Warwick (イギリス)
  • Year and Date: 2008-06-12
• [Presentation] Large deviation for the Ginzburg-Landau∇φinterface model with a conservation law (2008)
  • Author(s): 西川貴雄
  • Organizer: 研究集会「Hydrodynamics and fluctuations in interacting partcle systems」
  • Place of Presentation: Budapest University of Technology and Economics (ハンガリー)
  • Year and Date: 2008-03-29
• [Presentation] Large deviation for the Ginzburg-Landau∇φinterface model with a conservation law (2007)
  • Author(s): 西川貴雄
  • Organizer: 研究集会「大規模相互作用系の確率解析」
  • Place of Presentation: 九州大学
  • Year and Date: 2007-10-25
• [Presentation] Large deviation for the Ginzburg-Landau∇φinterface model with a conservation law (2007)
  • Author(s): 西川貴雄
  • Organizer: 研究集会「Dirichlet Forms, Stochastic Analysis & Interacting Systems」
  • Place of Presentation: Berlin Techinical University (ドイツ)
  • Year and Date: 2007-09-20