Particle systems with interaction

• Project/Area Number: 19540114
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Chiba University
• Principal Investigator: TANEMURA Hideki Chiba University, 大学院・理学研究科, 教授 (40217162)
• Co-Investigator(Kenkyū-buntansha): KONNO Norio 横浜国立大学, 工学研究院, 教授 (80205575) ; KATORI Makoto 中央大学, 理工学部, 教授 (60202016) ; SASAMOTO Tomohiro 千葉大学, 大学院・理学研究科, 准教授 (70332640)
• Project Period (FY): 2007 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2007: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 確率過程 / 無限粒子系 / ランダム行列 / 非衝突過程 / ダイソン模型 / ベッセル過程 / 拡散過程 / 行列値過程 / Sturm-Liouville作用素 / パフィアン過程 / 彷徨過程

Research Abstract

A stochastic process is called determinantal if its correlation functions are represented by determinants. During the research we proved that for any fixed configuration the noncolliding Brownian motion and the noncolliding squared Bessel process are determinantal. When number of particle is infinite, we gave sufficient conditions so that the noncolliding processes are exist and have continuous paths. We also showed the relaxation phenomena for the processes.

Research Products

• [Journal Article] Noncolliding squared Bessel processes (2011)
  • Author(s): Makoto Katori, Hideki Tanemura
  • Journal Title: J.Stat.Phys. 142 Pages: 149-172
  • Peer Reviewed
• [Journal Article] Noncolliding squared Bessel processes (2011)
  • Author(s): Makoto Katori
  • Journal Title: Journal of Statistical Physics Volume: 142 Pages: 149-172
  • Peer Reviewed
• [Journal Article] Non-equilibrium dynamics of Dyson's model with an infinite number of particles (2010)
  • Author(s): Makoto Katori, Hideki Tanemura
  • Journal Title: Commun.Math.Phys. 293 Pages: 469-497
  • Peer Reviewed
• [Journal Article] Non-equilibrium dynamics of Dyson's model with an infinite number of particles (2010)
  • Author(s): Makoto katori, Hideki Tanemura
  • Journal Title: Commun.Math.Phys. 293 Pages: 469-497
  • Peer Reviewed
• [Journal Article] Non-equilibrium dynamics of Dyson's model with an infinite number of particles (2010)
  • Author(s): Makoto Katori
  • Journal Title: Communications of Mathematical Physics 293 Pages: 469-497
  • Peer Reviewed
• [Journal Article] Zeros of Airy function and relaxation process (2009)
  • Author(s): Makoto Katori, Hideki Tanemura
  • Journal Title: J.Stat.Phys. 136 Pages: 1177-1204
  • Peer Reviewed
• [Journal Article] 非衝突過程、行列値過程、行列式過程 (2009)
  • Author(s): Makoto Katori, Hideki Tanemura
  • Journal Title: 数学 第61巻第3号 Pages: 225-247
  • NAID: 10026415164
  • Peer Reviewed
• [Journal Article] Zeros of Airy function and relaxation process (2009)
  • Author(s): Makoto katori, Hideki Tanemura
  • Journal Title: J.Stat.Phys. 136 Pages: 1177-1204
  • Peer Reviewed
• [Journal Article] 非衝突過程、行列値過程、行列式過程 (2009)
  • Author(s): Makoto katori, Hideki Tanemura
  • Journal Title: 数学 第61巻第3号 Pages: 225-247
  • NAID: 10026415164
• [Journal Article] Zeros of Airy function and relaxation process (2009)
  • Author(s): Makoto Katori
  • Journal Title: Journal of Statistical Physics 136 Pages: 1177-1204
  • Peer Reviewed
• [Journal Article] 非衝突過程、行列値過程、行列式過程 (2009)
  • Author(s): 香取眞理
  • Journal Title: 数学(日本数学会和文雑誌) 61 Pages: 225-247
  • NAID: 10026415164
  • Peer Reviewed
• [Journal Article] Two Bessel Bridges Conditioned Never to Collide, Double Dirichlet Series, and Jacobi Theta Function (2008)
  • Author(s): Katori, Makoto
  • Journal Title: Journal of Statistical Physics 131 Pages: 1067-1083
  • Peer Reviewed
• [Journal Article] Noncolliding Brownian motion and determinantal processes (2007)
  • Author(s): Makoto Katori, Hideki Tanemura
  • Journal Title: J.Stat.Phys. 129 Pages: 1233-1277
  • Peer Reviewed
• [Journal Article] Infinite Systems of Non-Colliding Generalized Meanders and Riemann-Liouville Differintegrals (2007)
  • Author(s): Makoto Katori, Hideki Tanemura
  • Journal Title: Probab.Th.Rel.Fields 138 Pages: 113-156
  • Peer Reviewed
• [Journal Article] Noncolliding Brownian motion and determinantal processes (2007)
  • Author(s): Makoto katori, Hideki Tanemura
  • Journal Title: J.Stat.Phys. 129 Pages: 1233-1277
  • Peer Reviewed
• [Journal Article] Infinite Systems of Non-Colliding Generalized Meanders and Riemann-Liouville Differintegrals (2007)
  • Author(s): Makoto katori, Hideki Tanemura
  • Journal Title: Probab. Th.Rel.Fields 138 Pages: 113-156
  • Peer Reviewed
• [Journal Article] Infinite systems of noncolliding generalized meanders and Riemann-Liouville differintegrals (2007)
  • Author(s): Katori, M.
  • Journal Title: Probability Theory and Related Fields 138 Pages: 113-156
  • Peer Reviewed
• [Journal Article] Noncolliding Brownian motion and determinantal processes (2007)
  • Author(s): Katori, M.
  • Journal Title: Journal of Statistical Physics 129 Pages: 1233-1277
  • Peer Reviewed
• [Journal Article] Dynamics of a tagged particle in the asymmetric exclusion process with the step initial condition (2007)
  • Author(s): Imamura, T.
  • Journal Title: Joumal of Statistical Physics 129 Pages: 1055-1080
  • Peer Reviewed
• [Presentation] Martingale Representation of determinantal processes (2011)
  • Author(s): 種村秀紀
  • Organizer: Workshop on Infinite Dimensional Analysis and Quantum Probability
  • Place of Presentation: National Institute for Mathematical Sciences(韓国,大田)
  • Year and Date: 2011-01-11
• [Presentation] Martingale Representation of determinantal processes (2011)
  • Author(s): Hideki Tanemura
  • Organizer: Infinite Dimensional Analysis and Quantum Probability
  • Place of Presentation: 韓国数理科学研究所
  • Year and Date: 2011-01-11
• [Presentation] Complex Brownian motion Representation of the Dyson Model (2010)
  • Author(s): 種村秀紀
  • Organizer: 34th Conference on Stochastic Processes and Their Applcations
  • Place of Presentation: Senri Life Science Building(大阪)
  • Year and Date: 2010-09-10
• [Presentation] Dyson's model with an infinite number of particles (2009)
  • Author(s): 種村秀紀
  • Organizer: Probability and Stochastic Process
  • Place of Presentation: インド統計研究所(インド、デリー)
  • Year and Date: 2009-11-27
• [Presentation] Noncolliding processes and Random Matrices (2009)
  • Author(s): 種村秀紀
  • Organizer: Selfsimilar processes and their applications
  • Place of Presentation: ボン・パスツールセンター(フランス、アンジェ)
  • Year and Date: 2009-07-24
• [Presentation] Non-equilibrium dynamics of Dyson's model (2009)
  • Author(s): 種村秀紀
  • Organizer: Random Processes and Systems
  • Place of Presentation: 忠北国立大学(韓国,忠北)
  • Year and Date: 2009-02-14
• [Presentation] Non-equilibrium dynamics of Dyson's model (2009)
  • Author(s): Tanemura, Hideki
  • Organizer: Infite Dimensional Analysis and Quantum Probability
  • Place of Presentation: 忠北国立大学(韓国)
  • Year and Date: 2009-01-14
• [Presentation] Non-equilibrium dynamics of Dyson's model (2009)
  • Author(s): 種村秀紀
  • Organizer: Random Processes and Systems
  • Place of Presentation: 忠北国立大学 (韓国, 忠北)
• [Presentation] Noncolliding processes and Random Matrices (2009)
  • Author(s): 種村秀紀
  • Organizer: Selfsimilar processes and their applications
  • Place of Presentation: ボン・パスツールセンター (フランス、アンジェ)
• [Presentation] Dyson's model with an infinite number of particles (2009)
  • Author(s): 種村秀紀
  • Organizer: Probability and Stochastic Process
  • Place of Presentation: インド統計研究所 (インド、デリー)
• [Remarks] ホームページ等
  • URL: http://www.math.s.chiba-u.ac.jp/~tanemura/
• [Remarks]
  • URL: http://www.math.s.chiba-u.ac.jp/tanemura/index.html
• [Remarks]
  • URL: http://www.math.s.chiba-u.ac.jp/~tanemura/index.html
• [Remarks]
  • URL: http://www.math.s.chiba-u.ac.jp/~tanemura/
• [Remarks]
  • URL: http://www.math.s.chiba-u.ac.jp/~tanemura/