Studies on hydrodynamic limit of lattice gas

• Project/Area Number: 18740052
• 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: Osaka University
• Principal Investigator: NAGAHATA Yukio Osaka University, 基礎工学研究科, 助教 (50397725)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥2,940,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥240,000); Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2007: ¥800,000 (Direct Cost: ¥800,000); Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
• Keywords: 確率論 / 確率過程論 / 格子気体 / 流体力学極限 / マルコフ過程 / スペクトルギャップ / 拡散係数

Research Abstract

格子気体の流体力学極限の研究を行った。その中でも特に流体力学極限の証明の中で鍵になる次の二つのことを調べた。(1)ある一般的な条件の下で極限の方程式を決定する拡散係数についてその性質を研究し、滑らかな関数であることが証明できた。(2)スペクトルギャップの評価を行い流体力学極限の証明には十分な結果が得られた。

Research Products

• [Journal Article] Regularity of the diffusion coefficient matrix for lattice gas reversible under Gibbs measures with mixing condition (2007)
  • Author(s): Y.Nagahata
  • Journal Title: Communications in Mathematical Physics 273, No.3 Pages: 637-650
  • Peer Reviewed
• [Journal Article] Regularity of the diffusion coefficient matrix for lattice gas reversible under Gibbs measures with mixing condition. (2007)
  • Author(s): Yukio NAGAHATA
  • Journal Title: Communications in Mathematical Physics 273 Pages: 637-650
  • Peer Reviewed
• [Journal Article] Regularity of the diffusion coefficient matrix for generalized exclusion process (2006)
  • Author(s): Y.Nagahata
  • Journal Title: Stochastic Processes and their Application 116 Pages: 957-982
  • Peer Reviewed
• [Journal Article] Regularity of the diffusion coefficient matrix for generalized exclusion process. (2006)
  • Author(s): Yukio NAGAHATA
  • Journal Title: Stochastic Processes and their Application 116 Pages: 957-982
• [Presentation] zero-range processのスペクトルギャップについて (2008)
  • Author(s): 永幡幸生
  • Organizer: 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] Central limit theorem for a class of linear systems (2008)
  • Author(s): 永幡幸生
  • Organizer: マルコフ過程とその応用
  • Place of Presentation: 兵庫県立大学
  • Year and Date: 2008-10-19
• [Presentation] Central limit theorem for a class of linear systems (2008)
  • Author(s): 永幡幸生
  • Organizer: 日独共同研究Stochastic Analysis and Applications 2008
  • Place of Presentation: 九州大学
  • Year and Date: 2008-09-09
• [Presentation] ある zero range process のスペクトルギャップについて (2008)
  • Author(s): Yukio NAGAHATA
  • Organizer: 無限粒子系、確率場の諸問題III
  • Place of Presentation: 岡山大学
  • Year and Date: 2008-01-09
• [Presentation] Central limit theorem for a class of linear systems (2008)
  • Author(s): Y.Nagahata
  • Organizer: マルコフ過程とその応用
  • Place of Presentation: 兵庫県立大学神戸キャンパス
• [Presentation] Central limit theorem for a class of linear systems (2008)
  • Author(s): Y.Nagahata
  • Organizer: 日独共同研究Stochastic Analysis and Applications 2008
  • Place of Presentation: 九州大学 西新プラザ
• [Presentation] ある zero range process のスペクトルギャップについて (2007)
  • Author(s): 永幡幸生
  • Organizer: 2007年度確率論シンポジウム
  • Place of Presentation: 放送大学熊本学習センター
  • Year and Date: 2007-12-12
• [Presentation] Spectral gap for zero range process with jump rate g(x)=x^=\gamma (2007)
  • Author(s): Yukio NAGAHATA
  • Organizer: Stochastic Analysis on Large scale Interacting Systems
  • Place of Presentation: 九州大学
  • Year and Date: 2007-10-23
• [Presentation] Spectral gap for zero range process with jump rate g(x)=x^=\gamma (2007)
  • Author(s): Yukio NAGAHATA
  • Organizer: Dirichlet Forms, Stochastic Analysis and Interacting Systems
  • Place of Presentation: T.U. Berlin
  • Year and Date: 2007-09-18
• [Presentation] Regularity of the diffusion coefficient for lattice gas reversible under Gibbs measures with mixing condition (2007)
  • Author(s): Yukio NAGAHATA
  • Organizer: 97th statistical mechanics conference
  • Place of Presentation: Rutgers University
  • Year and Date: 2007-05-08
• [Presentation] Spectral gap for zero range process with jump rate $g(x)=x^\gamma$ (2007)
  • Author(s): Y.Nagahata
  • Organizer: Stochastic Analysis on Large Scale Interacting Systems
  • Place of Presentation: 九州大学 西新プラザ
• [Presentation] Spectral gap for zero range process with jump rate $g(x)=x^\gamma$ (2007)
  • Author(s): Y.Nagahata
  • Organizer: Dirichlet Forms, Stochastic Analysis and Interacting Systems
  • Place of Presentation: T. U. Berlin
• [Presentation] Regularity of the diffusion coefficient matrix for lattice gas reversible under Gibbs measure with mixing condition (2007)
  • Author(s): Y.Nagahata
  • Organizer: 97th statistical mechanics conference
  • Place of Presentation: Rutgers University