Study on asymptotic behavior of stochastic interface models

• Project/Area Number: 23740086
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Keio University
• Principal Investigator: SAKAGAWA Hironobu 慶應義塾大学, 理工学部, 講師 (60348810)
• Project Period (FY): 2011 – 2013
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000); Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: 確率論 / 統計力学 / 相分離界面 / Gibbs測度 / Gauss過程 / 界面モデル / 相転移 / ギブス測度 / 自由エネルギー

Research Abstract

In this research, we considered several stochastic models on lattice and studied its asymptotic behavior for the mathematical analysis of phase separating interface and membrane. We first considered Laplacian phi model as a model of membrane and studied its free energy under the effect of two types of external potentials. We also considered a Gaussian process which appears in the time evolution of gradient phi interface model and obtained estimates on its persistence probability.

Research Products

• [Journal Article] Persistence probability for a class of Gaussian processes related to random interface models (2015)
  • Author(s): Hironobu Sakagawa
  • Journal Title: Advances in Applied Probability Volume: (掲載受理)
  • Peer Reviewed
• [Journal Article] Persistence probability for a class of Gaussian processes related to random interface models (2015)
  • Author(s): Hironobu Sakagawa
  • Journal Title: Advances in Applied Probability Volume: Vol.47, No.1
  • Peer Reviewed
• [Journal Article] On the free energy of a Gaussian membrane model with external potentials (2012)
  • Author(s): Hironobu Sakagawa
  • Journal Title: J. Stat. Phys Volume: Vol.147, no.1 Pages: 18-34
  • Peer Reviewed
• [Journal Article] On the free energy of a Gaussian membrane model with external potentials (2012)
  • Author(s): Hironobu Sakagawa
  • Journal Title: Journal of Statistical Physics Volume: 147 Pages: 18-34
  • Peer Reviewed
• [Presentation] Persistence probability for a class of Gaussian processes related to random in terface models (2013)
  • Author(s): 坂川 博宣
  • Organizer: Stochastic Analysis on Large Scale Interacting Systems
  • Place of Presentation: University of Tokyo
  • Year and Date: 2013-11-22
• [Presentation] Persistence probability for a class of Gaussian processes related to random interface models (2013)
  • Author(s): Hironobu Sakagawa
  • Organizer: Stochastic Analysis on Large Scale Interacting Systems
  • Place of Presentation: University of Tokyo
  • Invited
• [Presentation] Persistence probability for a class of Gaussian processes related to random in terface models (2012)
  • Author(s): 坂川 博宣
  • Organizer: 無限粒子系と確率場の諸問題VIII(short communication)
  • Place of Presentation: 奈良女子大学
  • Year and Date: 2012-10-20
• [Presentation] On the free energy of a Gaussian membrane model with external potentials (2012)
  • Author(s): 坂川 博宣
  • Organizer: 数理物理と確率解析
  • Place of Presentation: 湘南国際村センター
  • Year and Date: 2012-03-12
• [Presentation] Persistence probability for a class of Gaussian processe related to random interface models
  • Author(s): 坂川 博宣
  • Organizer: 無限粒子系と確率場の諸問題VIII (short communication)
  • Place of Presentation: 奈良女子大学
• [Presentation] On the free energy of a Gaussian membrane model with external forces
  • Author(s): 坂川博宣
  • Organizer: 数理物理と確率解析
  • Place of Presentation: 湘南国際村センター