Scaling limits for non-reversible and non-gradient systems

• 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
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000); Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 流体力学極限 / 揺動問題 / 非勾配型 / 国際研究者交流 / デンマーク：カナダ：フランス：ハンガリー / スケール極限 / 確率過程 / 非勾配型モデル / 平衡揺動問題 / 国際情報交換 / フランス

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] 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 Volume: 40 Pages: 543-560
  • DOI: 10.1007/978-1-4471-4863-0_23
  • ISBN: 9781447148623, 9781447148630
  • Peer Reviewed
• [Journal Article] Fluctuations in an evolutional model of two-dimensional Young diagrams (2013)
  • Author(s): T. Funaki, M. Sasada, M. Sauer and B. Xie
  • Journal Title: Stoch. Proc. Appl. Volume: 123 Issue: 4 Pages: 1229-1275
  • DOI: 10.1016/j.spa.2012.12.005
  • Peer Reviewed
• [Journal Article] Macroscopic energy diffusion for a chain of anharmonic oscillators (2013)
  • Author(s): Stefano Olla
  • Journal Title: Probability Theory and Related Fields Volume: not yet decided Issue: 3-4 Pages: 721-775
  • DOI: 10.1007/s00440-012-0469-5
  • Peer Reviewed
• [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] Spectral gap for multi-species exclusion processes (2011)
  • Author(s): Yukio Nagahata
  • Journal Title: Journal of Statistical Physics Volume: 143 Issue: 2 Pages: 381-398
  • DOI: 10.1007/s10955-011-0176-0
  • Peer Reviewed
• [Journal Article] Hydrodynamic limit for exelusion processes with velocity (2011)
  • Author(s): 佐々田槙子
  • Journal Title: Markov processes and related fields Volume: 17-3 Pages: 391-428
  • Peer Reviewed
• [Journal Article] Macroscopic energy diffusion for a chain of anharmonic oscillators,Stefano Olla
  • Author(s): Makiko SASADA
  • Journal Title: Probability theory and related fields
• [Journal Article] On the spectral gap of the Kac walk and other binary collision processes on d-dimensional lattice
  • Author(s): 佐々田槙子
  • Journal Title: Proceeding of the conference "Infinite Analysis" Volume: (掲載決定)
  • Peer Reviewed
• [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: 数理物理と確率解析
  • Place of Presentation: 湘南国際村センター(神奈川県)
  • Year and Date: 2012-03-12
• [Presentation] Hydrodynamic limit for exelusion processes with velocity (2012)
  • Author(s): 佐々田槙子
  • Organizer: ESF-JSPS Frontier Science Conference Series for Young Researchers Mathematics for Innovation : Large and Complex Systems
  • Place of Presentation: フォーシーズンズホテル・椿山荘(東京都)
  • Year and Date: 2012-03-03
• [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] 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(招待講演)
  • Year and Date: 2012-01-29
• [Presentation] Spectral gap for energy exchange models with rate functions approaching zero (2011)
  • Author(s): 佐々田槙子
  • Organizer: 10th workshop on Stochastic Analysis on Large Scale Interacting Systems
  • Place of Presentation: 高知大学(招待講演)
  • Year and Date: 2011-12-05
• [Presentation] 速度を持つ粒子系に対する流体力学極限 (2011)
  • Author(s): 佐々田槙子
  • Organizer: 日本数学会統計数学分科会特別講演
  • Place of Presentation: 信州大学(招待講演)
  • Year and Date: 2011-09-28
• [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
• [Presentation] Scaling limits for exclusion processes and evolutional models of Young diagrams (2011)
  • Author(s): 佐々田槙子
  • Organizer: Infinite Analysis 11
  • Place of Presentation: 東京大学数理科学研究科(招待講演)
  • Year and Date: 2011-07-26
• [Presentation] Spectral gap for stochastic energy exchange models with degenerate rate functions
  • Author(s): 佐々田槙子
  • Organizer: 11th workshop on Stochastic Analysis on Large Scale Interacting Systems
  • Place of Presentation: Graduate School of Mathematical Sciences, University of Tokyo
  • Invited
• [Presentation] 退化放物型方程式の流体力学極限による導出
  • Author(s): 佐々田槙子
  • Organizer: 異常拡散の数理
  • Place of Presentation: 京都大学数理解析研究所
  • Invited
• [Presentation] Stochastic energy exchange models with degenerate rate functions
  • Author(s): 佐々田槙子
  • Organizer: International Congress on Mathematical Physics ICMP2012
  • Place of Presentation: Aalborg, Denmark
  • Invited
• [Presentation] Microscopic dynamics for the porous medium equation and other degenerate parabolic equations
  • Author(s): 佐々田槙子
  • Organizer: MSJ-KMS Joint Meeting 2012
  • Place of Presentation: Centennial Hall, Kyushu University Medical School
  • Invited
• [Presentation] Mixing rates of stochastic energy exchange models with degenerate rate functions
  • Author(s): 佐々田槙子
  • Organizer: Nonequilibrium Statistical Mechanics: Mathematical Understanding and Numerical Simulation
  • Place of Presentation: Banff International Research Station
  • Invited
• [Presentation] ハミルトン系と流体力学極限
  • 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
  • Invited