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Comprehensive and integrated research of problems motivated by statistical mechanics with stochastic analysis

Research Project

Project/Area Number 17204011
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionKyushu University

Principal Investigator

OSADA Hirofumi  Kyushu University, 大学院・数理学研究院, 教授 (20177207)

Co-Investigator(Kenkyū-buntansha) FUNAKI Tadahisa  東京大学, 大学院・数理科学研究科, 教授 (60112174)
SHINODA Masato  奈良女子大学, 理学部, 准教授 (50271044)
KUMAGAI Takashi  京都大学, 大学院・理学研究科, 教授 (90234509)
SHIRAI Tomoyuki  九州大学, 大学院・数理学研究科, 教授 (70302932)
HARA Takashi  九州大学, 大学院・数理学研究科, 教授 (20228620)
FUKAI Yasunari  九州大学, 大学院・数理学研究科, 助教 (00311837)
UTIYAMA Kohei  東京工業大学, 大学院・理工学研究科, 教授 (00117566)
MATSUMOTO Hiroyuki  名古屋大学, 大学院・情報科学研究科, 教授 (00190538)
TANEMURA Hideki  千葉大学, 理学部, 教授 (40217162)
NAGAHATA Yukio  大阪大学, 大学院・基礎工学研究科, 助教 (50397725)
HIGUCHI Yasunari  神戸大学, 理学部, 教授 (60112075)
MITOMA Itaru  佐賀大学, 理工学部, 教授 (40112289)
SUGIURA Makoto  琉球大学, 理学部, 准教授 (70252228)
KONNNO Norio  横浜国立大学, 大学院・工学研究院, 教授 (80205575)
KOMORIYA Keishi  筑波大学, 数理物質科学研究科, 助教 (40323258)
OTOBE Yoshiki  信州大学, 理学部, 講師 (30334882)
YOSHIDA Nobuo  京都大学, 大学院・理学研究科, 准教授 (40240303)
LIANG Song  筑波大学, 数理物質科学研究科, 准教授 (60324399)
HANDA Kenji  佐賀大学, 理工学部, 准教授 (10238214)
Project Period (FY) 2005 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥26,910,000 (Direct Cost: ¥20,700,000、Indirect Cost: ¥6,210,000)
Fiscal Year 2008: ¥6,760,000 (Direct Cost: ¥5,200,000、Indirect Cost: ¥1,560,000)
Fiscal Year 2007: ¥6,760,000 (Direct Cost: ¥5,200,000、Indirect Cost: ¥1,560,000)
Fiscal Year 2006: ¥6,760,000 (Direct Cost: ¥5,200,000、Indirect Cost: ¥1,560,000)
Fiscal Year 2005: ¥6,630,000 (Direct Cost: ¥5,100,000、Indirect Cost: ¥1,530,000)
Keywords確率論 / 解析学 / 統計力学 / 無限粒子系 / 確率解析 / 確率場 / 確率力学系
Research Abstract

統計力学は、膨大な自由度-数学的には無限自由度-をもつ系を研究対象とする。この研究では、統計力学に動機づけられた諸問題を、とくに無限次元確率力学系を中心として、確率解析の手法で統一的に研究し、確率場、相互作用粒子系、極限定理に関係する様々な結果を得た。さらに、これらの研究を契機として、Bessel確率積分やフラクタル構造領域の劣ガウス型熱核の評価など、確率解析の理論を発展させた。

Report

(5 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • Research Products

    (50 results)

All 2008 2007 2006 2005

All Journal Article (36 results) (of which Peer Reviewed: 19 results) Presentation (11 results) Book (3 results)

  • [Journal Article] Variance of the linear statistics of the Ginibre random point field2008

    • Author(s)
      H.Osada and T. Shirai
    • Journal Title

      RIMS Kokyuroku Bessatsu B6

      Pages: 193-200

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Decay of correlations in nearest-neighbor self-avoiding walk, percolation2008

    • Author(s)
      T. Hara
    • Journal Title

      lattice trees and animals. Ann. Probab 36, no.2

      Pages: 530-593

    • Related Report
      2008 Final Research Report
  • [Journal Article] A scaling limit for weakly pinned Gaussian random walks2008

    • Author(s)
      T. Funaki
    • Journal Title

      RIMS Kokyuroku Bessatsu B6

      Pages: 97-109

    • Related Report
      2008 Annual Research Report 2008 Final Research Report
  • [Journal Article] Heat kernel estimates for strongly recurrent random walk on random media2008

    • Author(s)
      T. Kumagai, J. Misumi
    • Journal Title

      J. Theoret. Probab 4

      Pages: 910-935

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Heat kernel estimates for jump processes of mixed types on metric measure spaces2008

    • Author(s)
      Z.-Q. Chen and T. Kumagai
    • Journal Title

      Probab. Theory Relat. Fields 140

      Pages: 277-317

    • Related Report
      2008 Final Research Report
  • [Journal Article] Random walk on the incipient infinite cluster for oriented percolation in high dimensions2008

    • Author(s)
      M.T. Barlow, A.A. J\'arai, T. Kumagai and G. Slade
    • Journal Title

      Comm. Math. Phys. 278

      Pages: 385-431

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Wiener integrals for centered powers of Bessel processes, II2008

    • Author(s)
      T. Funaki, et al.
    • Journal Title

      ALEA Lat. Am. J. Probab. Mat. Stat. 1

      Pages: 225-240

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Variance of the linear statistics of the Ginibre random point field2008

    • Author(s)
      H. Osada, T. Shirai
    • Journal Title

      RIMS Kokyuroku Bessatsu B6

      Pages: 193-200

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Heat kernel estimates for strongly recurrent random walk on random media2008

    • Author(s)
      T. Kumagai, J. Misumi
    • Journal Title

      J. Theoret. Probab. 4

      Pages: 910-935

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Heat kernel estimates for jump processes of mixed types on metric measure spaces2008

    • Author(s)
      Z.Q.Chen and T.Kumagai
    • Journal Title

      Probab.Theory Relat.Fields 140

      Pages: 277-317

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic expansion of the one-loop approximation of the Chern-Simons integral in an abstract Wiener space setting2007

    • Author(s)
      I. Mitoma, S.Nishikawa
    • Journal Title

      J. Funct. Anal. 253, no.2

      Pages: 729-771

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Regularity of the diffusion coefficient matrix for lattice gas reversible under Gibbs measures with mixing condition2007

    • Author(s)
      Y. Nagahata
    • Journal Title

      Communications in Mathematical Physics 273

      Pages: 637-650

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Infinite Systems of Non-Colliding Generalized Meanders and Riemann-Liouville Differintegrals2007

    • Author(s)
      M. Katori and H. Tanemura
    • Journal Title

      Probab. Theory Relat. Fields 138

      Pages: 113-156

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Regularity of the diffusion coefficient matrix for lattice gas reversible under Gibbs measures with mixing condition2007

    • Author(s)
      Y.Nagahata
    • Journal Title

      Communications in Mathematical Physics 273

      Pages: 637-650

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article]2007

    • Author(s)
      M.Katori and H.Tanemura
    • Journal Title

      Probab.Theory Relat.Fields 138

      Pages: 113-156

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Multi-state epidemic processes on complex networks2006

    • Author(s)
      N. Masuda, N. Konno
    • Journal Title

      J. Theoret. Biol. 243-1

      Pages: 64-75

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Continuous-time quantum walks on trees in quantum probability theory2006

    • Author(s)
      N. Konno
    • Journal Title

      Infin. Dimens. Anal. Quantum Prob. Relat. Top. 9-2

      Pages: 287-297

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Nash-type inequalities and heat kernels for non-local Dirichlet forms2006

    • Author(s)
      J. Hu, T. Kumagai
    • Journal Title

      Kyushu J. Math. 60

      Pages: 245-265

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Random walk on the incipient infinite cluster on trees2006

    • Author(s)
      M. Barlow, T. Kumagai
    • Journal Title

      Illinois J. Math. 50、1-4

      Pages: 33-65

    • Related Report
      2008 Final Research Report
  • [Journal Article] A trace theorem for Dirichlet forms on fractals2006

    • Author(s)
      T. Kumagai, M. Hino
    • Journal Title

      J. Func. Anal. 238-2

      Pages: 578-611

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stochastic partial differential equations with two reflecting walls2006

    • Author(s)
      Y. Otobe
    • Journal Title

      J. Math. Sci. Univ. Tokyo 13(no.2)

      Pages: 129-144

    • NAID

      120006905998

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Multi-state epidemic processes on complex networks2006

    • Author(s)
      N.Masuda, N.Konno
    • Journal Title

      J. Theoret. Biol. 243・1

      Pages: 64-75

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Continuous-time quantum walks on trees in quantum probability theory2006

    • Author(s)
      N.Konno
    • Journal Title

      Infin. Dimens. Anal. Quantum Prob. Relat. Top. 9-2

      Pages: 287-297

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Wiener integrals for centered powers of Bessel processes, II2006

    • Author(s)
      T.Funaki, et al.
    • Journal Title

      ALEA Lat. Am. J. Probab. Mat. Stat. 1

      Pages: 225-240

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Nash-type inequalities and heat kernels for non-local Dirichlet forms.2006

    • Author(s)
      J.Hu, T.Kumagai
    • Journal Title

      Kyushu J. Math 60

      Pages: 245-265

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Random walk on the incipient infinite cluster on trees.2006

    • Author(s)
      M.Barlow, T.Kumagai
    • Journal Title

      IIIinois J. Math 50,1-4

      Pages: 33-65

    • Related Report
      2006 Annual Research Report
  • [Journal Article] A trace theorem for Dirichlet forms on fractals2006

    • Author(s)
      T.Kumagai, M.Hino
    • Journal Title

      J. Func. Anal. 238-2

      Pages: 578-611

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Wiener integrals for centered powers of Bassel processes, I2006

    • Author(s)
      T.Funaki, et al.
    • Journal Title

      Markov Processes Related Fields (In press)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Stochastic Interface Models. In : Lectures on Probability Theory and Statistics and Statistics2005

    • Author(s)
      T. Funaki, et.al.
    • Journal Title

      Springer Lect. Notes Math. 58-12

      Pages: 103-274

    • Related Report
      2008 Final Research Report
  • [Journal Article] Characterization of sub-Gaussian heat kernel estimates on strongly recurrent graphs2005

    • Author(s)
      M. Barlow, T. Kumagai et.al.
    • Journal Title

      Comm. Pure Appl. Math. 58-12

      Pages: 1642-1677

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A new type of limit theorems for the one-dimensional quantum random walk2005

    • Author(s)
      N. Konno
    • Journal Title

      J. Math. Soc. Japan 57-4

      Pages: 1179-1195

    • NAID

      10017178197

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Limit theorem for continuous-time quantum walk on the line2005

    • Author(s)
      N.Konno
    • Journal Title

      Phys. Rev. E(3) 72-2

      Pages: 26113-26119

    • Related Report
      2008 Final Research Report
  • [Journal Article] A new type of limit theorems for the one-dimensional quantum random walk2005

    • Author(s)
      N.Konno
    • Journal Title

      J.Math.Soc.Japan 57・4

      Pages: 1179-1195

    • NAID

      10017178197

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Limit theorem for continuous-time quantum walk on the line2005

    • Author(s)
      N.Konno
    • Journal Title

      Phys.REv.E(3) 72-2

      Pages: 26113-26119

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Stochastic Interface Models. In: Lectures on Probability Theory and Statistics and Statistics2005

    • Author(s)
      T.Funaki
    • Journal Title

      Springer Lect.Notes Math., 1869

      Pages: 103-274

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Characterization of sub-Gaussian heat kernel estimates on strongly recurrent graphs2005

    • Author(s)
      M.Barlow, et al.
    • Journal Title

      Comm.Pure Appl.Math. 58-12

      Pages: 1642-1677

    • Related Report
      2005 Annual Research Report
  • [Presentation] Scaling limits for weakly pinned random walks with two large deviationminimizers2008

    • Author(s)
      T. Funaki
    • Organizer
      Workshop "Interplay of Analysis and Probability in Physics"
    • Place of Presentation
      Mathematisches Forschungsinstitut Oberwolfach
    • Year and Date
      2008-12-04
    • Related Report
      2008 Final Research Report
  • [Presentation] Hydrodynamic limit for the $\nabla \phi$ interface model via two-scale approach2008

    • Author(s)
      T. Funaki
    • Organizer
      Trimester "Interacting particle systems, statistical mechanics and probability theory"
    • Place of Presentation
      Institut Henri Poincar\'e, Paris
    • Year and Date
      2008-11-24
    • Related Report
      2008 Final Research Report
  • [Presentation] Stochastic Differential Equations on the Sierpinski Carpet2008

    • Author(s)
      H.Osada
    • Organizer
      3rd Conference on Analysis and Probability on Fractals
    • Place of Presentation
      Cornell University
    • Year and Date
      2008-06-15
    • Related Report
      2008 Final Research Report
  • [Presentation] Stochastic Differential Equations on the Sierpinski Carpet2008

    • Author(s)
      H. Osada
    • Organizer
      3rd Conference on Analysis and. Probability on Fraotals
    • Place of Presentation
      Cornell University
    • Year and Date
      2008-06-15
    • Related Report
      2008 Annual Research Report
  • [Presentation] Stochastic calculus on manifolds, graphs, and Random structures2007

    • Author(s)
      T. Kumagai
    • Organizer
      Diffusion on the scaling limits of critical percolation clusters in the diamond hierarchical lattice
    • Place of Presentation
      Bonn(ドイツ)Hausdorff研究所
    • Year and Date
      2007-10-12
    • Related Report
      2008 Final Research Report
  • [Presentation] Scaling limits for weakly pinned Gaussian random walks2007

    • Author(s)
      T. Funaki
    • Organizer
      The Mittag-Leffler Seminar, Institut Mittag-Leffler
    • Place of Presentation
      The Royal Swedish Academy of Sciences
    • Year and Date
      2007-10-04
    • Related Report
      2008 Final Research Report
  • [Presentation] SPDE with distributions of L\'evy processes as its invariant measures, Stochastic Partial Differential Equations2007

    • Author(s)
      T. Funaki
    • Organizer
      Workshop at Mittag-Leffler Institute
    • Place of Presentation
      Sweden
    • Year and Date
      2007-09-13
    • Related Report
      2008 Final Research Report
  • [Presentation] Interacting Brownian motions related to random matrices2007

    • Author(s)
      H. Osada
    • Organizer
      Stochastic Processes and its applications
    • Place of Presentation
      イリノイ大学
    • Year and Date
      2007-08-07
    • Related Report
      2008 Final Research Report 2007 Annual Research Report
  • [Presentation] Recent developments in random walks2007

    • Author(s)
      T. Kumagai
    • Organizer
      Heat kernel estimates and Harnack inequalities for jump processes
    • Place of Presentation
      Durham(英国)、LMS Durham symposium
    • Year and Date
      2007-07-06
    • Related Report
      2008 Final Research Report
  • [Presentation] Concentrations under scaling limits for weakly pinned Gaussian random walks, Groupe de travail, Processus Stochastiques, Matrices Al\'eatoires"2007

    • Author(s)
      T. Funaki
    • Organizer
      Laboratoire de Probabilit\'es et Mod\`eles Al\'eatoires des Universit\'es Pierre et Marie Curie et Denis Diderot
    • Place of Presentation
      Paris
    • Year and Date
      2007-03-23
    • Related Report
      2008 Final Research Report
  • [Presentation] Random motion of Winterbottom-like shape2005

    • Author(s)
      T. Funaki
    • Organizer
      Stochastic Analysis and Non-Classical Random Processes
    • Place of Presentation
      Mathematisches Forschungsinstitut Oberwolfach
    • Year and Date
      2005-05-13
    • Related Report
      2008 Final Research Report
  • [Book] ルベーグ積分入門-使うための理論と演習2006

    • Author(s)
      吉田伸生
    • Total Pages
      246
    • Publisher
      遊星社
    • Related Report
      2006 Annual Research Report
  • [Book] 確率微分方程式2005

    • Author(s)
      舟木直久
    • Publisher
      岩波書店
    • Related Report
      2008 Final Research Report
  • [Book] 確率微分方程式2005

    • Author(s)
      舟木 直久
    • Publisher
      岩波書店
    • Related Report
      2005 Annual Research Report

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Published: 2005-04-01   Modified: 2016-04-21  

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