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Analysis of random phenomena and its applications from the viewpoint of determinantal point processes

Research Project

Project/Area Number 18H01124
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Review Section Basic Section 12010:Basic analysis-related
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) 種村 秀紀  慶應義塾大学, 理工学部(矢上), 教授 (40217162)
香取 眞理  中央大学, 理工学部, 教授 (60202016)
Project Period (FY) 2018-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥16,770,000 (Direct Cost: ¥12,900,000、Indirect Cost: ¥3,870,000)
Fiscal Year 2022: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2021: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2020: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2019: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2018: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Keywords行列式点過程 / ガウス型解析関数 / ガウス型ローラン級数 / Weyl-Heisenberg点過程 / ワイヤレスネットワーク / ダイソンブラウン運動 / ランダム複体 / 複素バーガーズ方程式 / ランダム解析関数 / 全域非輪体 / マーラー測度 / 多重シュラムレブナー発展 / 超一様性 / ベッセル関数 / 摂動格子 / Weyl-Heisenberg点過程 / SINR / 点過程 / 点過程の剛性 / Weyl-Heisenberg 点過程 / harmonic ensemble / spherical ensemble
Outline of Final Research Achievements

A stochastic model in which the probability distribution is described by a determinant, obtained by abstracting the repulsive nature of electrons (fermions), is called a determinant point process. It is known that the structure of the determinantal point process is hidden in many problems that are seemingly unrelated to electrons. In this study, we analyze random phenomena of such various determinantal point processes, especially focusing on asymptotic behavior and limit theorems, which are central issues in probability theory, and apply them to specific problems such as wireless networks.

Academic Significance and Societal Importance of the Research Achievements

行列式点過程は、数理科学の中の多くの分野で現れる負の相関をもつランダム現象を記述する確率モデルである.行列式点過程の構造および性質を深く掘り下げることによりランダムな現象を解析した本研究は,数学としての確率論の一分野に貢献するとともに,機械学習やワイヤレスネットワークなど実世界の問題にも応用された例を鑑みると,未来のテクノロジーや社会の様々な分野で活用されるポテンシャルも期待される.

Report

(6 results)
  • 2023 Final Research Report ( PDF )
  • 2022 Annual Research Report
  • 2021 Annual Research Report
  • 2020 Annual Research Report
  • 2019 Annual Research Report
  • 2018 Annual Research Report
  • Research Products

    (48 results)

All 2024 2023 2022 2021 2020 2019 2018 Other

All Int'l Joint Research (3 results) Journal Article (16 results) (of which Peer Reviewed: 16 results,  Open Access: 12 results) Presentation (25 results) (of which Int'l Joint Research: 19 results,  Invited: 21 results) Remarks (1 results) Funded Workshop (3 results)

  • [Int'l Joint Research] シンガポール国立大学(シンガポール)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] 国立音響研究所(オーストリア)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] Leiden University(オランダ)

    • Related Report
      2018 Annual Research Report
  • [Journal Article] Stochastic differential equations for infinite particle systems of jump type with long range interactions2024

    • Author(s)
      ESAKI Syota、TANEMURA Hideki
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 76 Issue: 1 Pages: 283-336

    • DOI

      10.2969/jmsj/90289028

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Partial isometries, duality, and determinantal point processes2022

    • Author(s)
      Katori Makoto、Shirai Tomoyuki
    • Journal Title

      Random Matrices: Theory and Applications

      Volume: 11 Issue: 03 Pages: 1-70

    • DOI

      10.1142/s2010326322500253

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Zeros of the i.i.d.Gaussian Laurent Series on an Annulus: Weighted Szeg? Kernels and Permanental-Determinantal Point Processes2022

    • Author(s)
      Katori Makoto、Shirai Tomoyuki
    • Journal Title

      Communications in Mathematical Physics

      Volume: - Issue: 3 Pages: 1099-1151

    • DOI

      10.1007/s00220-022-04365-2

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Local universality of determinantal point processes on Riemannian manifolds2022

    • Author(s)
      Makoto Katori and Tomoyuki Shirai
    • Journal Title

      Proc. Japan Acad. Ser. A Math. Sci.

      Volume: 98 Pages: 95-100

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Expected Number of Zeros of Random Power Series with Finitely Dependent Gaussian Coefficients2022

    • Author(s)
      Noda, K., Shirai, T
    • Journal Title

      J Theor Probab

      Volume: ー Issue: 3 Pages: 1534-1554

    • DOI

      10.1007/s10959-022-01203-y

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Functional Equations Solving Initial-Value Problems of Complex Burgers-Type Equations for One-Dimensional Log-Gases2022

    • Author(s)
      Endo Taiki、Chuo University, Japan、Katori Makoto、Sakuma Noriyoshi、Chuo University, Japan、Nagoya City University, Japan
    • Journal Title

      Symmetry, Integrability and Geometry: Methods and Applications

      Volume: 18 Pages: 1-22

    • DOI

      10.3842/sigma.2022.049

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Local number variances and hyperuniformity of the Heisenberg family of determinantal point processes2021

    • Author(s)
      Matsui Takato、Katori Makoto、Shirai Tomoyuki
    • Journal Title

      Journal of Physics A: Mathematical and Theoretical

      Volume: 54 Issue: 16 Pages: 165201-165201

    • DOI

      10.1088/1751-8121/abecaa

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Three phases of multiple SLE driven by non-colliding Dyson’s Brownian motions2021

    • Author(s)
      Katori Makoto、Koshida Shinji
    • Journal Title

      Journal of Physics A: Mathematical and Theoretical

      Volume: 54 Issue: 32 Pages: 325002-325002

    • DOI

      10.1088/1751-8121/ac0dee

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Gaussian free fields coupled with multiple SLEs driven by stochastic log-gases2021

    • Author(s)
      Katori Makoto and Koshida Shinji
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 87 Pages: 315-340

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Scaling limit for determinantal point processes on spheres2020

    • Author(s)
      Makoto Katori and Tomoyuki Shirai
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: B79 Pages: 123-138

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Conformal welding problem, flow line problem, and multiple Schramm?Loewner evolution2020

    • Author(s)
      Katori Makoto、Koshida Shinji
    • Journal Title

      Journal of Mathematical Physics

      Volume: 61 Issue: 8 Pages: 083301-083301

    • DOI

      10.1063/1.5145357

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Zeta functions of periodic cubical lattices and Cyclomatic-like polynomials2020

    • Author(s)
      Yasuaki Hiraoka, Hiroyuki Ochiai and Tomoyuki Shirai
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 84 Pages: 93-121

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Two-Dimensional Elliptic Determinantal Point Processes and Related Systems2019

    • Author(s)
      Makoto Katori
    • Journal Title

      Commun. Math. Phys.

      Volume: 371 Issue: 3 Pages: 1283-1321

    • DOI

      10.1007/s00220-019-03351-5

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the zeros of the Macdonald functions2019

    • Author(s)
      Hamana Yuji、Matsumoto Hiroyuki、Shirai Tomoyuki
    • Journal Title

      Opuscula Mathematica

      Volume: 39 Issue: 3 Pages: 361-382

    • DOI

      10.7494/opmath.2019.39.3.361

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Macdonald denominators for affine root systems, orthogonal theta functions, and elliptic determinantal point processes2019

    • Author(s)
      Makoto Katori
    • Journal Title

      Journal of Mathematical Physics

      Volume: 60 Issue: 1 Pages: 013301-013301

    • DOI

      10.1063/1.5037805

    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Zeta functions of periodic cubical lattices and cyclotomic-like polynomials2019

    • Author(s)
      Yasuaki Hiraoka, Hiroyuki Ochiai and Tomoyuki Shirai
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: 印刷中

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Presentation] Phase transition for a unidirectional elephant random walk with a pawer law memory,2024

    • Author(s)
      Hideki Tanemura
    • Organizer
      無限粒子系、確率場の諸問題XVII
    • Related Report
      2022 Annual Research Report
  • [Presentation] Phase transition for a unidirectional elephant random walk with a pawer law memory2024

    • Author(s)
      Hideki Tanemura
    • Organizer
      Interacting particle systems and SPDEs China-Japan Probability Workshop at BIMSA and YMSC
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Zeros of random power series with stationary Gaussian coefficients2024

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      French Japanese Conference on Probability and Interactions
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On a model of evolution of subspecies2023

    • Author(s)
      Hideki Tanemura
    • Organizer
      Boston-Keio-Tsinghua Workshop 2023 Probability and Statistics, Boston University
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Elephant random walk with a power law memory2023

    • Author(s)
      Hideki Tanemura
    • Organizer
      The 21st Symposium Stochastic Analysis on Large Scale Interaction Systems
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Zeros of Gaussian power series with dependent coefficients2023

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      The 21st Symposium Stochastic Analysis on Large Scale Interacting Systems
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Non-Hermitian matrix-valued processes and the regularized Fuglede-Kadison determiannt random-fields2023

    • Author(s)
      Makoto Katori
    • Organizer
      Random Operators and Related Topics
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Elliptic extensions in statistical and stochastic systems2023

    • Author(s)
      Makoto Katori
    • Organizer
      International Conference on Mathematical Methods in Physics (ICMMP23)
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Eigenvalues, eigenvector-overlaps, and regularized Fuglede--Kadison determinant of the non-Hermitian matrix-valued Brownian motion2023

    • Author(s)
      Makoto Katori
    • Organizer
      International Workshop `Random Matrices and Applications'
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Stochastic log-gases, multiple SLEs, and Gaussian free fields2023

    • Author(s)
      Makoto Katori
    • Organizer
      New Trends of Conformal theory from probability to gravity
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Zeros of random analytic functions with dependent Gaussian coefficients2021

    • Author(s)
      白井朋之
    • Organizer
      確率・ 統計・ 行列ワークショップ 彦根 2021
    • Related Report
      2021 Annual Research Report
  • [Presentation] アルファ行列式の正値性と点過程2021

    • Author(s)
      白井朋之
    • Organizer
      統計数理研共同研究ISMCRP2001「固有値分布と行列式点過程に基づく統計モデル」,統計数理研究所
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] Orthogonal theta functions associated with affine root systems and determinantal point processes2021

    • Author(s)
      Makoto Katori
    • Organizer
      CIRM Conference - Modern Analysis Related to Root Systems with Applications
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 円環上のガウス型解析関数とパーマネント・行列式点過程2021

    • Author(s)
      香取眞理
    • Organizer
      東京確率論セミナー
    • Related Report
      2021 Annual Research Report
  • [Presentation] Hyperuniformity of the determinantal point processes associated with the Heisenberg group2021

    • Author(s)
      香取眞理
    • Organizer
      2021 RIMS共同研究研究会「量子場の数理とその周辺」
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Duality of determinantal point processes2020

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      Workshop on "Random matrices, Determinantal point processes and Gaussian analytic functions"
    • Related Report
      2020 Annual Research Report
  • [Presentation] Limit theorems for determinantal point processes2019

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      International Conference on Mathematical Methods in Physics , Marrakesh, Morocco.
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Limit theorems for determinantal point processes2019

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      A Probability Conference on Random Matrices and Related Topics, KIAS, Seoul, Korea
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Limit theorems for persistence diagrams2019

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      Seminar at KTH Royal Institute of Technology, Sweden
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Partial isometries, duality, and determinantal point processes2019

    • Author(s)
      Makoto Katori
    • Organizer
      Japanese-German Open Conference on Stochastic Analysis 2019, Sept.2-6, 2019, Fukuoka University, Japan
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Partial Isometries, Duality, and Determinantal Point Processes2019

    • Author(s)
      Makoto Katori
    • Organizer
      Workshop on Random Matrices, Stochastic Geometry and Related Topics
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Systems of hard balls with long-range interactions2019

    • Author(s)
      Hideki Tanemura
    • Organizer
      Workshop on Random Matrices, Stochastic Geometry and Related Topics
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Dynamic determinantal point processes2019

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      Ajou-Kyushu joint workshop on Industrial Mathematics
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Universality of determinantal point processes on Riemannian manifolds2018

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      RIMS Joint Research (Open): 17th International Symposium Stochastic Analysis on Large Scale Interacting Systems
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Limit theorems for determinantal point processes2018

    • Author(s)
      Tomoyuki Shirai
    • Organizer
      エルゴード理論研究会
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Remarks] https://imi.kyushu-u.ac.jp/~shirai/

    • Related Report
      2019 Annual Research Report
  • [Funded Workshop] Workshop on Probabilistic Methods in Statistical Mechanics of Random Media and Random Fields2019

    • Related Report
      2019 Annual Research Report
  • [Funded Workshop] Workshop on "Random matrices, stochastic geometry and related topics", NUS, Singapore. (Mar. 14th--16th, 2019)2019

    • Related Report
      2018 Annual Research Report
  • [Funded Workshop] International Conference on "Random matrices and their applications", (May. 21--25, 2018)2018

    • Related Report
      2018 Annual Research Report

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Published: 2018-04-23   Modified: 2025-01-30  

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