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Determinantal processes and their generalizations

Research Project

Project/Area Number 26287019
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypePartial Multi-year Fund
Section一般
Research Field Basic analysis
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) 脇 隼人  九州大学, マス・フォア・インダストリ研究所, 准教授 (00567597)
種村 秀紀  千葉大学, 大学院理学研究院, 教授 (40217162)
香取 眞理  中央大学, 理工学部, 教授 (60202016)
Co-Investigator(Renkei-kenkyūsha) MIYOSHI Naoto  東京工業大学, 情報理工学院, 教授 (20263121)
Research Collaborator OSADA Hirofumi  九州大学, 大学院数理学研究院, 教授 (20177207)
Project Period (FY) 2014-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥14,690,000 (Direct Cost: ¥11,300,000、Indirect Cost: ¥3,390,000)
Fiscal Year 2017: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2016: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2015: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2014: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Keywords行列式過程 / ギニブル点過程 / 再生核ヒルベルト空間 / パーム測度 / ワイヤレスネットワーク / 代数的力学系 / SLE / Dysonモデル / 確率論 / 行列式点過程 / セルラーネットワーク / ランダム行列 / ダイソンモデル / 行列式型マルチンゲール
Outline of Final Research Achievements

Determinantal point processes are one of the most important models of describing several phenomena that exhibit repulsion. We investigate theoretical aspects and also application aspects of determinantal point processes and their generalization. For example, we estimate the Signal-to-Interference-Ratio for the wireless network whose base stations are configurated by Ginibre point process, which is one of the most important determinantal point processes and has been used for the study of random matrices in physics.

Report

(5 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Annual Research Report
  • 2015 Annual Research Report
  • 2014 Annual Research Report
  • Research Products

    (30 results)

All 2018 2017 2016 2015 2014 Other

All Int'l Joint Research (4 results) Journal Article (11 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 10 results,  Open Access: 5 results,  Acknowledgement Compliant: 6 results) Presentation (11 results) (of which Int'l Joint Research: 7 results,  Invited: 7 results) Remarks (1 results) Funded Workshop (3 results)

  • [Int'l Joint Research] Leiden University(オランダ)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] Leiden University(オランダ)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] Aix Marseille University(France)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] Leiden University(オランダ)

    • Related Report
      2015 Annual Research Report
  • [Journal Article] Hydrodynamic Limit of Multiple SLE2018

    • Author(s)
      Hotta Ikkei、Katori Makoto
    • Journal Title

      Journal of Statistical Physics

      Volume: 171 Issue: 1 Pages: 166-188

    • DOI

      10.1007/s10955-018-1996-y

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Tail asymptotics of signal-to-interference ratio distribution in spatial cellular network models2017

    • Author(s)
      Naoto Miyoshi, Tomoyuki Shirai
    • Journal Title

      Probability and Mathematical Statistics

      Volume: 37 Issue: 2 Pages: 431-453

    • DOI

      10.19195/0208-4147.37.2.12

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Quasi-symmetries and rigidity for determinantal point processes associated with de Branges spaces2017

    • Author(s)
      Alexander I. Bufetov and Tomoyuki Shirai
    • Journal Title

      Proceedings of the Japan Academy, Ser. A Math. Sci.

      Volume: 93 Issue: 1 Pages: 1-5

    • DOI

      10.3792/pjaa.93.1

    • NAID

      40021065833

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Solvable and algebraic systems on infinite ladder2016

    • Author(s)
      Tomoyuki Shirai and Evgeny Verbitskiy
    • Journal Title

      Indagationes Mathematicae

      Volume: 27 Issue: 5 Pages: 1116-1183

    • DOI

      10.1016/j.indag.2016.02.003

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Spatial Modeling and Analysis of Cellular Networks Using the Ginibre Point Process: A Tutorial2016

    • Author(s)
      Naoto Miyoshi and Tomoyuki Shirai
    • Journal Title

      IEICE Transactions on Communications

      Volume: E99.B Issue: 11 Pages: 2247-2255

    • DOI

      10.1587/transcom.2016NEI0001

    • NAID

      130005268118

    • ISSN
      0916-8516, 1745-1345
    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Elliptic Bessel processes and elliptic Dyson models realized as temporally inhomogeneous processes2016

    • Author(s)
      Makoto Katori
    • Journal Title

      Journal of Mathematical Physics

      Volume: 57 Issue: 10 Pages: 103302-103302

    • DOI

      10.1063/1.4964253

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] The mean spectral measures of random Jacobi matrices related Gaussian beta ensembles2015

    • Author(s)
      Trinh Khanh Duy and Tomoyuki Shirai
    • Journal Title

      Electoric Communications in Probability

      Volume: 20 Issue: none Pages: 1-13

    • DOI

      10.1214/ecp.v20-4252

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Ginibre-type point processes and their asymptotic behavior2015

    • Author(s)
      Tomoyuki Shirai
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 67 Issue: 2 Pages: 763-787

    • DOI

      10.2969/jmsj/06720763

    • NAID

      130005069903

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Downlink coverage probability in a cellular network with Ginibre deployed base stations and Nakagami-m fading channels2015

    • Author(s)
      Naoto Miyoshi and Tomoyuki Shirai
    • Journal Title

      13th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks (WiOpt 2015), Mumbai, India, May 25-29, 2015.

      Volume: 未定

    • Related Report
      2014 Annual Research Report
  • [Journal Article] Determinantal martingales and correlations of noncolliding random walks2015

    • Author(s)
      Makoto Katori
    • Journal Title

      Journal of Statistical Physics

      Volume: 159 Issue: 1 Pages: 21-42

    • DOI

      10.1007/s10955-014-1179-4

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Cores of Dirichlet forms related to random matrix theory2014

    • 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

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Presentation] Machine learning for DPP2018

    • Author(s)
      白井朋之
    • Organizer
      Workshop on "Random matrices, determinantal processes and their related topics"
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Determinantal point processes associated with extended kernels and spanning trees on series-parallel graphs2017

    • Author(s)
      白井朋之
    • Organizer
      Function theory and dynamics of point processes, Euler International Mathematical Institute, St. Petersburg, Russia.
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Hydrodynamic Limits of Multiple SLE2017

    • Author(s)
      香取眞理
    • Organizer
      Tokyo-Seoul Conference in Mathematics ーProbability Theoryー
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Determinantal point processes associated with reproducing kernel Hilbert spaces2017

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      Random Matrices and Determinantal Process
    • Place of Presentation
      CIRM, Marseille, France
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Persistent homology for point processes2016

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      Random matrices, determinantal processes and their related topics
    • Place of Presentation
      B-con Plaza, Oita, Japan
    • Year and Date
      2016-03-06
    • Related Report
      2015 Annual Research Report
  • [Presentation] Elliptic Bessel Process and Elliptic Dyson Model Realized as Temporally Inhomogeneous Processes2015

    • Author(s)
      Makoto Katori
    • Organizer
      14th International Symposium, Stochastic Analysis on Large Scale Interacting Systems
    • Place of Presentation
      RIMS, Kyoto University
    • Year and Date
      2015-10-28
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Stochastic differential equations related to random matrix theory2015

    • Author(s)
      Hideki Tanemura
    • Organizer
      14th International Symposium, Stochastic Analysis on Large Scale Interacting Systems
    • Place of Presentation
      RIMS, Kyoto University
    • Year and Date
      2015-10-28
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Downlink Coverage Probability in a Cellular Network with Ginibre Deployed Base Stations and Nakagami-m Fading Channels2015

    • Author(s)
      Naoto Miyoshi
    • Organizer
      WiOpt 2015 : The 13th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks
    • Place of Presentation
      Indian Institute of Technology, Bombay, Mumbai, India
    • Year and Date
      2015-05-28
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Elliptic determinant evaluations and diffusion processes2015

    • Author(s)
      香取眞理
    • Organizer
      Spectra of Random Operators and Related Topics
    • Place of Presentation
      京都大学
    • Year and Date
      2015-01-09
    • Related Report
      2014 Annual Research Report
  • [Presentation] Airy random point field に対する無限次元確率微分方程式2014

    • Author(s)
      種村秀紀
    • Organizer
      2014年度日本数学会総合分科会
    • Place of Presentation
      広島大学
    • Year and Date
      2014-09-25
    • Related Report
      2014 Annual Research Report
  • [Presentation] Absolute Continuity and Singularity for the Ginibre Point Process and its Palm Measures2014

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      UK-Japan Stochastic Analysis School
    • Place of Presentation
      University of Warwick
    • Year and Date
      2014-09-02
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Remarks] Tomoyuki Shirai

    • URL

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

    • Related Report
      2016 Annual Research Report
  • [Funded Workshop] Workshop on "Random matrices, determinantal processes and their related topics"2018

    • Related Report
      2017 Annual Research Report
  • [Funded Workshop] 14thSALSIS The 14th workshop on "Stochastic Analysis on Large Scale Interacting Systems2015

    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2015-10-26
    • Related Report
      2015 Annual Research Report
  • [Funded Workshop] Workshop on "Probabilistic models with determinantal structure"2015

    • Place of Presentation
      九州大学マス・フォア・インダストリ研究所
    • Year and Date
      2015-04-30
    • Related Report
      2015 Annual Research Report

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Published: 2014-04-04   Modified: 2022-02-16  

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