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Study on stochastic processes with determinantal structure

Research Project

Project/Area Number 22340020
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKyushu University

Principal Investigator

SHIRAI Tomoyuki  九州大学, マス・フォア・インダストリ研究所, 教授 (70302932)

Co-Investigator(Kenkyū-buntansha) TANEMURA Hideki  千葉大学, 大学院・理学系研究科, 教授 (40217162)
KATORI Makoto  中央大学, 理工学部, 教授 (60202016)
Co-Investigator(Renkei-kenkyūsha) OSADA Hirofumi  九州大学, 大学院・数理学研究院, 教授 (20177207)
Project Period (FY) 2010-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥13,780,000 (Direct Cost: ¥10,600,000、Indirect Cost: ¥3,180,000)
Fiscal Year 2013: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2012: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2011: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2010: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
KeywordsGinibre 点過程 / 行列式点過程 / Palm 測度 / 絶対連続性 / 相関関数 / ランダム行列 / アルファ行列式 / パフィアン点過程 / ダイソンモデル / オコネル過程 / Ginibre点過程 / パーム測度 / 多時刻相関関数 / O'Connell過程 / ランダム解析関数 / 行列式過程 / 非衝突過程 / ガウス型解析関数
Research Abstract

Correlation functions of the eigenvalues of certain random matrices can be expressed by using determinant. A point configuration whose correlation functions are determinants has repulsive property and is called a determinantal point process. Many mathematical objects can be described as a determinantal point process and analyzed precisely. We study the Ginibre point process, which is a typical model of determinantal point process, and we use this determinantal point process instead of poisson point process as a model of base stations of a cellular network and analyze it. We investigated determinantal point processes from both theoretical and applied mathematical points of view.

Report

(5 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (47 results)

All 2014 2013 2012 2011 2010 Other

All Journal Article (15 results) (of which Peer Reviewed: 15 results) Presentation (29 results) (of which Invited: 7 results) Book (2 results) Remarks (1 results)

  • [Journal Article] Note on the spectrum of discrete Schrodinger operators2014

    • Author(s)
      Fumio Hiroshima, Itaru Sasaki, Tomoyuki Shirai, Akito Suzuki
    • Journal Title

      Journal of Math-for-Industry

      Volume: 5 Pages: 105-108

    • NAID

      120007101192

    • URL

      http://j-mi.org/articles/index/11

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Remarks on α -deteminants via SDP relaxation2013

    • Author(s)
      Takayuki Osogami, Tomoyuki Shirai, Hayato Waki
    • Journal Title

      Journal of Math-for-Industry

      Volume: 5 Pages: 1-10

    • URL

      http://j-mi.org/articles/index/14

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Correlation functions for zeros of a Gaussian power series and Pfaffians2013

    • Author(s)
      Sho Matsumoto, Tomoyuki Shirai
    • Journal Title

      Electronic Journal of Probability

      Volume: 18(49) Issue: none Pages: 1-18

    • DOI

      10.1214/ejp.v18-2545

    • URL

      http://ejp.ejpecp.org/article/view/2545

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Complex Brownian motion representation of the Dyson model2013

    • 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

    • Related Report
      2013 Annual Research Report 2013 Final Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Remarks on α-determinant via SDP relaxation2013

    • Author(s)
      Takayuki Osogami, Tomoyuki Shirai and Hayato Waki
    • Journal Title

      Journal of Math-for-Industry

      Volume: 5

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Limit theorems for random analytic functions and their zeros2012

    • Author(s)
      Tomoyuki Shirai
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: 34 Pages: 335-359

    • URL

      http://www.kurims.kyoto-u.ac.jp/~kenkyubu/bessatsu/B34-contents.pdf

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Limit theorem for random analytic functions and their zeros2012

    • Author(s)
      Tomoyuki Shirai
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: 34

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Survival probability of mutually killing Brownian motions and the O'Connell process2012

    • Author(s)
      Makoto Katori
    • Journal Title

      J. Stat. Phys

      Volume: 147 Issue: 1 Pages: 206-223

    • DOI

      10.1007/s10955-012-0472-3

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] System of complex Brownian motions associated with the O'Connell process2012

    • Author(s)
      Makoto Katori
    • Journal Title

      J. Stat. Phys

      Volume: 149 Issue: 3 Pages: 411-431

    • DOI

      10.1007/s10955-012-0602-y

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Noncolliding squared Bessel processes2011

    • 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

    • Related Report
      2013 Final Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Markov property of determinantal processes with extended sine, Airy, and Bessel kernels2011

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

      Markov processes and related fields

      Volume: 17 Pages: 541-580

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] O'Connell's process as a vicious Brownian motion2011

    • Author(s)
      Makoto Katori
    • Journal Title

      Phys. Rev. E

      Volume: 84, 061144 Issue: 6 Pages: 1-11

    • DOI

      10.1103/physreve.84.061144

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Non-equilibrium dynamics of Dyson's model with an infinite number of particles2010

    • Author(s)
      Hideki Tanemura, Makoto Katori
    • Journal Title

      Communications in Mathematical Physics

      Volume: 293 Pages: 469-497

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Limit theorem for random analytic functions and their zeros

    • Author(s)
      Tomoyuki Shirai
    • Journal Title

      To appear in RIMS Kokyuroku Bessatsu

      Volume: (to appear)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Determinantal correlations of Brownian paths in the plane with nonintersection condition on their loop-erased parts

    • Author(s)
      Makiko Sato, Makoto Katori
    • Journal Title

      Physical Review E

      Volume: (未定 accepted)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] Zeros of a certain Gaussian power series2013

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      The 8th Jikji Workshop "Infinite Dimensional Analysis and Quantum Probability"
    • Place of Presentation
      NIMS, Daejeon, Korea
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Applications of determinantal point processes2013

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      Forum "Math-for-Industry" 2013 -The Impact of Applications on Mathematics-
    • Place of Presentation
      Nishijin Plaza, Kyushu University
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Remarks on α-determinantal point fields2013

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      The 12th workshop on Stochastic Analysis on Large Scale Interacting Systems
    • Place of Presentation
      University of Tokyo
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Determinantal martingales and determinantal processes2013

    • Author(s)
      Makoto Katori
    • Organizer
      Workshop on ``Random analytic functions, random matrices, and determinantal point processes''
    • Place of Presentation
      Ito Campus, Kyushu University
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Strong Markov property of determinatal processes associated with extended kernels2013

    • Author(s)
      Hideki Tanemura
    • Organizer
      The 12th workshop on Stochastic Analysis on Large Scale Interacting Systems
    • Place of Presentation
      University of Tokyo
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] On the zeros of random analytic functions2013

    • Author(s)
      白井朋之
    • Organizer
      Markov processes and stochastic analysis
    • Place of Presentation
      京都大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Vicious Brownian motion, O'Connell's process, and equilibrium Toda lattice2012

    • Author(s)
      Makoto Katori
    • Organizer
      Interacting particle systems, growth models and random matrices
    • Place of Presentation
      The University of Warwick
    • Year and Date
      2012-03-21
    • Related Report
      2011 Annual Research Report
  • [Presentation] Stochastic differential equations associated with infinite particles with long ranged interaction2012

    • Author(s)
      種村秀紀
    • 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)
    • Related Report
      2012 Annual Research Report
  • [Presentation] Determinantal formula appearing in non-determinantal process2012

    • Author(s)
      香取眞理
    • Organizer
      研究集会 「ランダム作用素のスペクトルと関連する話題」
    • Place of Presentation
      京都大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Ginibre point process and its Palm measures : absolute continuity and singularity2011

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      10^<th> workshop on Stochastic Analysis on Large Scale Interacting Particle Systems
    • Place of Presentation
      高知大学
    • Year and Date
      2011-12-07
    • Related Report
      2011 Annual Research Report
  • [Presentation] Determinantal Processes and Entire Functions2011

    • Author(s)
      Hideki Tanemura
    • Organizer
      Quantum and classical random processes
    • Place of Presentation
      Centro de Ciencias de Benasque Pedro Pascual
    • Year and Date
      2011-05-23
    • Related Report
      2011 Annual Research Report
  • [Presentation] Determinantal point processes and zeros of analytic functions2010

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      The international conference on Functions in Number Theory and Their Probabilistic Aspects
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-12-16
    • Related Report
      2010 Annual Research Report
  • [Presentation] Determinantal point processes and the zeros of analytic functions

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      Functions in Number Theory and Their Probabilistic Aspects
    • Place of Presentation
      Kyoto University
    • Related Report
      2013 Final Research Report
  • [Presentation] On the zeros of certain complex Wiener integrals

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      伊都確率論シンポジウム
    • Place of Presentation
      九州大
    • Related Report
      2013 Final Research Report
  • [Presentation] Random analytic functions and their zeros

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      analysis on Graphs in sendai
    • Place of Presentation
      東北大
    • Related Report
      2013 Final Research Report
  • [Presentation] Random analytic functions and their zeros

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      The Eve of IMI and FM
    • Place of Presentation
      九州大
    • Related Report
      2013 Final Research Report
  • [Presentation] Positivity for α -determinant via SDP relaxation

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      IBM
    • Place of Presentation
      東京基礎件
    • Related Report
      2013 Final Research Report
  • [Presentation] Ginibre point processes and its Palm measures : absolute continuity and singularity

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      10th Workshop on Stochastic Analysis on Large Scale Interacting Systems
    • Place of Presentation
      高知大
    • Related Report
      2013 Final Research Report
  • [Presentation] ガウス型べき級数の零点過程の相関関数

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      研究集会「確率論シンポジウム」
    • Place of Presentation
      京都大数理研
    • Related Report
      2013 Final Research Report
  • [Presentation] On the zeros of random analytic functions

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      研究集会「マルコフ過程と確率解析」
    • Place of Presentation
      京都大理学部
    • Related Report
      2013 Final Research Report
  • [Presentation] Correlation functions for zeros of a Gaussian power series and Pfaffians

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      Seminars on determinantal processes and related topics
    • Place of Presentation
      Technische Universitat Munchen
    • Related Report
      2013 Final Research Report
  • [Presentation] Zeros of a certain Gaussian power series

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      the 8th Jikji Workshop"Infinite Dimensional Analysis and Quantum Probability"
    • Place of Presentation
      NIMS, Daejeon, Korea
    • Related Report
      2013 Final Research Report
  • [Presentation] Fermion and boson point processes and related topics

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      量子場の数理とその周辺
    • Place of Presentation
      京都大数理研
    • Related Report
      2013 Final Research Report
  • [Presentation] Applications of determinantal point processes

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      FMI2013"The Impact of Applications on Mathematics"
    • Place of Presentation
      九州大西新プラザ
    • Related Report
      2013 Final Research Report
  • [Presentation] Remarks on alpha-determinantal point fields

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      The 12th workshop on Stochastic Analsys on Large Scale Interacting Systems
    • Place of Presentation
      東京大数理科学研究科
    • Related Report
      2013 Final Research Report
  • [Presentation] Cellular network model and alpha-Ginibre point processes

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      Workshop on"Random analytic functions, random matrices, and determinantal processes"
    • Place of Presentation
      九州大伊都
    • Related Report
      2013 Final Research Report
  • [Presentation] Alpha-determinantal point field associated with Green kernel

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      研究会「確率論シンポジウム」
    • Place of Presentation
      京都大数理研
    • Related Report
      2013 Final Research Report
  • [Presentation] Vicious Brownian motion, O'Connells' process, and equilibrium Toda lattice

    • Author(s)
      Makoto Katori
    • Organizer
      EPSRC Symposium Workshop, Interacting particle systems, growth models and random matrices
    • Place of Presentation
      The University of Warwick
    • Related Report
      2013 Final Research Report
  • [Presentation] Stochastic differential equiations related to soft-edge scaling limit

    • Author(s)
      Hideki Tanemura
    • Organizer
      EPSRC Symposium Workshop, "Interacting particle systems, growth models and random matrices"
    • Place of Presentation
      The University of Warwick
    • Related Report
      2013 Final Research Report
  • [Book] 確率論ハンドブック,第11 章確率論と数理物理(SLE (Schramm-Loewner-Evolution) (分担執筆)2012

    • Author(s)
      白井朋之, 香取眞理
    • Publisher
      丸善
    • Related Report
      2013 Final Research Report
  • [Book] 確率論ハンドブック (第11章.確率論と数理物理,SLE(Schramm-Loewner Evolution) 担当)2012

    • Author(s)
      白井朋之・香取眞理
    • Total Pages
      579
    • Publisher
      丸善出版
    • Related Report
      2012 Annual Research Report
  • [Remarks]

    • URL

      http://imi.kyushu-u.ac.jp/~shirai/

    • Related Report
      2013 Final Research Report

URL: 

Published: 2010-08-23   Modified: 2019-07-29  

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