Scaling limits for non-reversible and non-gradient systems

2012 Fiscal Year Final Research Report

• Project/Area Number: 23840036
• 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: Keio University
• Principal Investigator: SASADA Makiko 慶應義塾大学, 理工学部, 助教 (00609042)
• Project Period (FY): 2011 – 2012
• Keywords: 流体力学極限 / 揺動問題 / 非勾配型

Research Abstract

We study the energy diffusion in a chain of an-harmonic oscillators where the Hamiltonian dynamics is perturbed by a local energy conserving noise. We prove that under diffusive rescaling of space-time, energy fluctuations diffuse and evolve following an

Research Products

• [Journal Article] On the spectral gap of the Kac walk and other binary collision processes on d-dimensional lattice (2013)
  • Author(s): Makiko SASADA
  • Journal Title: Symmetries, Integrable Systems and Representations, Springer Proceedings in Mathematics & Statistics Pages: 543-560
• [Journal Article] Spectral gap for multi-species exclusion processes (2011)
  • Author(s): Yukio NAGAHATA, Makiko SASADA
  • Journal Title: Journal of Statistical Physics Volume: 3 Pages: 381-398
  • Peer Reviewed
• [Journal Article] Hydrodynamic limit for exclusion processes with velocity (2011)
  • Author(s): Makiko SASADA
  • Journal Title: Markov processes and related fields Volume: 17 Pages: 391-428
• [Journal Article] Macroscopic energy diffusion for a chain of anharmonic oscillators,Stefano Olla
  • Author(s): Makiko SASADA
  • Journal Title: Probability theory and related fields
• [Presentation] ハミルトン系と流体力学極限 (2013)
  • Author(s): 佐々田 槙子
  • Organizer: 城崎新人セミナー
  • Place of Presentation: 兵庫県豊岡市 城崎総合支所
  • Year and Date: 2013-02-20
• [Presentation] Mixing rates of stochastic energy exchange models with degenerate rate functions (2012)
  • Author(s): Makiko SASADA
  • Organizer: Nonequilibrium Statistical Mechanics, Mathematical Understanding and Numerical Simulation, Banff International Research Station
  • Place of Presentation: Canada
  • Year and Date: 2012-11-14
• [Presentation] Microscopic dynamics for the porous medium equation and other degenerate parabolic equations (2012)
  • Author(s): Makiko SASADA
  • Organizer: MSJ-KMS Joint Meeting 2012
  • Place of Presentation: Centennial Hall, Kyushu UniversityMedical School
  • Year and Date: 2012-09-17
• [Presentation] Stochastic energy exchange models with degenerate rate functions (2012)
  • Author(s): Makiko SASADA
  • Organizer: International Congress on Mathematical Physics ICMP2012
  • Place of Presentation: Aalborg, Denmark
  • Year and Date: 2012-08-09
• [Presentation] 退化放物型方程式の流体力学極限による導出 (2012)
  • Author(s): 佐々田槙子
  • Organizer: RIMS共同研究 異常拡散の数理
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2012-07-19
• [Presentation] Spectral gap for stochastic energy exchange models with degenerate rate functions (2012)
  • Author(s): Makiko SASADA
  • Organizer: 11th Stochastic Analysis on Large Scale Interacting Systems
  • Place of Presentation: The University of Tokyo
  • Year and Date: 2012-07-05
• [Presentation] Kac walk とその他のbinary collision process に対するスペクトルギャップについて (2012)
  • Author(s): 佐々田槙子
  • 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] Kac walk とその他のbinary collision process に対するスペクトルギャップについて (2012)
  • Author(s): 佐々田槙子
  • Organizer: 新潟確率論ワークショップ
  • Place of Presentation: 新潟大学
  • Year and Date: 2012-01-29
• [Presentation] Spectral gap for energy exchange models with rate functions approaching zero (2011)
  • Author(s): Makiko SASADA
  • Organizer: 10th Stochastic Analysis on Large Scale Interacting Systems
  • Place of Presentation: Kochi University
  • Year and Date: 2011-09-05