Stochastic analysis of infinite particle systems in nonequilibruim

• Project/Area Number: 23540122
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Chiba University
• Principal Investigator: TANEMURA Hideki 千葉大学, 理学(系)研究科(研究院), 教授 (40217162)
• Co-Investigator(Renkei-kenkyūsha): KATORI Makoto 中央大学, 理工学部, 教授 (60202016) ; SASAMOTO Tomohiro 東京工業大学, 大学院理工学研究科, 准教授 (70332640)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000); Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2011: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: 行列式過程 / 確率微分方程式 / ダイソン模型 / エアリー過程 / ランダム行列 / ディリクレ形式 / 末尾シグマ加法族 / 非平衡系 / 無限粒子系 / 強マルコフ性 / エアリー点過程 / 相関関数 / 行列値過程 / マルコフ性 / 特殊関数 / 行列式点過程 / 無限次元確率微分方程式 / 多時刻相関関数

Outline of Final Research Achievements

We study existence and uniqueness of infinite dimensional stochastic differential equations (ISDEs). We clarified the relation between the uniqueness of solutions and the triviality of tail sigma fields. Applying the result, we obtained the uniqueness of strong solutions of ISDEs describing the systems of Brownian motions with long range interaction including logarithmic potential, and determined the Dirichlet forms associated with the systems.

Research Products

• [Journal Article] Cores of Dirichlet forms related to random matrix theory (2014)
  • Author(s): H. Osada, H. Tanemura
  • Journal Title: Proc. Japan Acad. Ser. A Math. Sci. Volume: 90 Issue: 10 Pages: 145-150
  • DOI: 10.3792/pjaa.90.145
  • NAID: 110009929943
  • Peer Reviewed / Open Access
• [Journal Article] Complex Brownian motion representation of the Dyson model (2013)
  • Author(s): Makoto Katori and Hideki Tanemura
  • Journal Title: Electron. Commun. Probab Volume: 18, no.4 Issue: none Pages: 1-16
  • DOI: 10.1214/ecp.v18-2554
  • URL: http://ecp.ejpecp.org/article/view/2554
  • Peer Reviewed
• [Journal Article] Markov property of determinantal processes with extended sine, Airy, and Bessel kernels (2011)
  • Author(s): Makoto Katori
  • Journal Title: Markov processes and related fields Volume: 17 Pages: 541-580
  • Peer Reviewed
• [Journal Article] Noncolliding processes, Matrix-valued process and determinatal processes (2011)
  • Author(s): Makoto Katori
  • Journal Title: SUGAKU EXPOSITIONS Volume: 24 Pages: 263-289
  • Peer Reviewed
• [Journal Article] Noncolliding squared Bessel processes (2011)
  • Author(s): Makoto Katori and Hideki Tanemura
  • Journal Title: J. Stat. Phys Volume: 142 Issue: 3 Pages: 592-615
  • DOI: 10.1007/s10955-011-0117-y
  • URL: http://link.springer.com/article/10.1007/s10955-011-0117-y
  • Peer Reviewed
• [Presentation] Airy random point field に対応する無限次元確率微分方程式 (2014)
  • Author(s): 種村 秀紀
  • Organizer: 日本数学会
  • Place of Presentation: 広島大学
  • Year and Date: 2014-09-25
• [Presentation] 末尾sigma-加法族と無限次元確率微分方程式の強解の存在と一意性 (2014)
  • Author(s): 種村 秀紀
  • Organizer: 日本数学会
  • Place of Presentation: 広島大学
  • Year and Date: 2014-09-25
• [Presentation] Strong Markov property of determinantal processes (2013)
  • Author(s): Hideki Tanemura
  • Organizer: 36th Conference on Stochastic Processes and Their Applcations
  • Place of Presentation: Eaton Humanities on the University of Colorado Boulder campus
• [Presentation] Complex Brownian motion representation of non-colliding diffusion processes (2013)
  • Author(s): 種村秀紀
  • Organizer: 日本数学会
  • Place of Presentation: 愛媛大学
• [Presentation] Strong Markov property of determinantal processes (2013)
  • Author(s): 種村秀紀
  • Organizer: 日本数学会
  • Place of Presentation: 愛媛大学
• [Presentation] Strong Markov property of determinantal processes associated with extended kernels (2013)
  • Author(s): Hideki Tanemura
  • Organizer: 12th Workshop on Stochastic Analysis on Large Scale Interacting System
  • Place of Presentation: 東京大学大学院数理科学研究科002号室
• [Presentation] Stochastic differential equations associated with infinite particles with long ranged interaction (2012)
  • Author(s): Hideki Tanemura
  • Organizer: The World Congress in Probability and Statistics
  • Place of Presentation: Grand Cevahir Hotel and Convention Center （イスタンブール、トルコ）
• [Presentation] Stochastic differential equations related to soft-edge scaling limit (2012)
  • Author(s): Hideki Tanemura
  • Organizer: Interacting particle systems, growth models and random matrices(招待講演)
  • Place of Presentation: Warwick（イギリス）
• [Presentation] Determinantal Processes and Entire Functions (2011)
  • Author(s): Hideki Tanemura
  • Organizer: Quantum and classical random processes(招待講演)
  • Place of Presentation: Benasque(スペイン)
• [Presentation] Infinite Particle Systems associated with Airy kernel (2011)
  • Author(s): Hideki Tanemura
  • Organizer: 10th Workshop on Stochastic Analysis on Large Scale Interacting System(招待講演)
  • Place of Presentation: 高知大学