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

• Project/Area Number: 18H01124
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Review Section: Basic Section 12010:Basic analysis-related
• Research Institution: Kyushu University
• Principal Investigator: 白井 朋之 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 2022)
• Budget Amount: ¥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: ガウス型解析関数 / 複素バーガーズ方程式 / 行列式点過程 / ランダム複体 / 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 Annual Research Achievements

CUEの固有値の一般化に対応するコンパクトリーマン多様体上の行列式点過程の極限定理について分担者の香取眞理氏と研究して、その行列式点過程の適切なスケール極限が、円板の定義関数のフーリエ変換を用いて表現される相関核に付随する普遍的な行列式点過程に弱収束することを示して執筆した論文が日本学士院紀要より出版された。また、円環領域のガウス型解析関数の零点について研究を行い、通常の円板領域のガウス型解析関数の零点と違う性質を持つ点過程について調べた論文が出版された。また、ガウス型解析関数の零点を点過程とみなして、それを平衡状態として不変にする時間発展の研究について、Subhro Ghosh 氏(NUS)、長田博文氏（中部大）らと、自然に定まるディリクレ形式の可閉性の議論と対数微分の可積分性についての評価を行い、特に高い次数の剛性を持つαガウス型解析関数についても議論を行った。野田航平氏（九大）とPeres-Viragらによって研究された円板上のガウス型解析関数の拡張にあたる、係数が独立でない定常ガウス過程からなるベキ級数として定まるガウス型解析関数の零点の個数の漸近挙動について詳しく調べた論文が出版された。ランダム全域非輪体を方体複体の設定で考察し、代数的力学系のエントロピーなどとの関連を視野に入れて考察した論文を執筆した。また、香取氏は遠藤氏と佐久間氏との共同研究において、３種類の1次元の対数ガスモデル(ダイソンブラウン運動など)の流体力学的極限を考察し、対応する測度値過程のコーシー変換が複素バーガース型の解となることを示した。

Research Progress Status

令和4年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

令和4年度が最終年度であるため、記入しない。

Research Products

• [Int'l Joint Research] シンガポール国立大学(シンガポール)
• [Int'l Joint Research] 国立音響研究所(オーストリア)
• [Int'l Joint Research] Leiden University(オランダ)
• [Journal Article] Stochastic differential equations for infinite particle systems of jump type with long range interactions (2024)
  • 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
  • Peer Reviewed / Open Access
• [Journal Article] Partial isometries, duality, and determinantal point processes (2022)
  • Author(s): Katori Makoto、Shirai Tomoyuki
  • Journal Title: Random Matrices: Theory and Applications Volume: 11 Issue: 03 Pages: 1-70
  • DOI: 10.1142/s2010326322500253
  • 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 Processes (2022)
  • 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
  • Peer Reviewed / Open Access
• [Journal Article] Local universality of determinantal point processes on Riemannian manifolds (2022)
  • Author(s): Makoto Katori and Tomoyuki Shirai
  • Journal Title: Proc. Japan Acad. Ser. A Math. Sci. Volume: 98 Pages: 95-100
  • Peer Reviewed / Open Access
• [Journal Article] Expected Number of Zeros of Random Power Series with Finitely Dependent Gaussian Coefficients (2022)
  • 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
  • Peer Reviewed / Open Access
• [Journal Article] Functional Equations Solving Initial-Value Problems of Complex Burgers-Type Equations for One-Dimensional Log-Gases (2022)
  • 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
  • Peer Reviewed / Open Access
• [Journal Article] Local number variances and hyperuniformity of the Heisenberg family of determinantal point processes (2021)
  • 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
  • Peer Reviewed / Open Access
• [Journal Article] Three phases of multiple SLE driven by non-colliding Dyson’s Brownian motions (2021)
  • 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
  • Peer Reviewed / Open Access
• [Journal Article] Gaussian free fields coupled with multiple SLEs driven by stochastic log-gases (2021)
  • Author(s): Katori Makoto and Koshida Shinji
  • Journal Title: Advanced Studies in Pure Mathematics Volume: 87 Pages: 315-340
  • Peer Reviewed / Open Access
• [Journal Article] Scaling limit for determinantal point processes on spheres (2020)
  • Author(s): Makoto Katori and Tomoyuki Shirai
  • Journal Title: RIMS Kokyuroku Bessatsu Volume: B79 Pages: 123-138
  • Peer Reviewed / Open Access
• [Journal Article] Conformal welding problem, flow line problem, and multiple Schramm?Loewner evolution (2020)
  • Author(s): Katori Makoto、Koshida Shinji
  • Journal Title: Journal of Mathematical Physics Volume: 61 Issue: 8 Pages: 083301-083301
  • DOI: 10.1063/1.5145357
  • Peer Reviewed / Open Access
• [Journal Article] Zeta functions of periodic cubical lattices and Cyclomatic-like polynomials (2020)
  • Author(s): Yasuaki Hiraoka, Hiroyuki Ochiai and Tomoyuki Shirai
  • Journal Title: Advanced Studies in Pure Mathematics Volume: 84 Pages: 93-121
  • Peer Reviewed
• [Journal Article] Two-Dimensional Elliptic Determinantal Point Processes and Related Systems (2019)
  • Author(s): Makoto Katori
  • Journal Title: Commun. Math. Phys. Volume: 371 Issue: 3 Pages: 1283-1321
  • DOI: 10.1007/s00220-019-03351-5
  • Peer Reviewed
• [Journal Article] On the zeros of the Macdonald functions (2019)
  • 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
  • Peer Reviewed / Open Access
• [Journal Article] Macdonald denominators for affine root systems, orthogonal theta functions, and elliptic determinantal point processes (2019)
  • Author(s): Makoto Katori
  • Journal Title: Journal of Mathematical Physics Volume: 60 Issue: 1 Pages: 013301-013301
  • DOI: 10.1063/1.5037805
  • Peer Reviewed
• [Journal Article] Zeta functions of periodic cubical lattices and cyclotomic-like polynomials (2019)
  • Author(s): Yasuaki Hiraoka, Hiroyuki Ochiai and Tomoyuki Shirai
  • Journal Title: RIMS Kokyuroku Bessatsu Volume: 印刷中
  • 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
• [Presentation] Phase transition for a unidirectional elephant random walk with a pawer law memory (2024)
  • Author(s): Hideki Tanemura
  • Organizer: Interacting particle systems and SPDEs China-Japan Probability Workshop at BIMSA and YMSC
  • Int'l Joint Research / Invited
• [Presentation] Zeros of random power series with stationary Gaussian coefficients (2024)
  • Author(s): Tomoyuki Shirai
  • Organizer: French Japanese Conference on Probability and Interactions
  • Int'l Joint Research / Invited
• [Presentation] On a model of evolution of subspecies (2023)
  • Author(s): Hideki Tanemura
  • Organizer: Boston-Keio-Tsinghua Workshop 2023 Probability and Statistics, Boston University
  • Int'l Joint Research / Invited
• [Presentation] Elephant random walk with a power law memory (2023)
  • Author(s): Hideki Tanemura
  • Organizer: The 21st Symposium Stochastic Analysis on Large Scale Interaction Systems
  • Int'l Joint Research / Invited
• [Presentation] Zeros of Gaussian power series with dependent coefficients (2023)
  • Author(s): Tomoyuki Shirai
  • Organizer: The 21st Symposium Stochastic Analysis on Large Scale Interacting Systems
  • Int'l Joint Research / Invited
• [Presentation] Non-Hermitian matrix-valued processes and the regularized Fuglede-Kadison determiannt random-fields (2023)
  • Author(s): Makoto Katori
  • Organizer: Random Operators and Related Topics
  • Int'l Joint Research / Invited
• [Presentation] Elliptic extensions in statistical and stochastic systems (2023)
  • Author(s): Makoto Katori
  • Organizer: International Conference on Mathematical Methods in Physics (ICMMP23)
  • Int'l Joint Research / Invited
• [Presentation] Eigenvalues, eigenvector-overlaps, and regularized Fuglede--Kadison determinant of the non-Hermitian matrix-valued Brownian motion (2023)
  • Author(s): Makoto Katori
  • Organizer: International Workshop `Random Matrices and Applications'
  • Int'l Joint Research / Invited
• [Presentation] Stochastic log-gases, multiple SLEs, and Gaussian free fields (2023)
  • Author(s): Makoto Katori
  • Organizer: New Trends of Conformal theory from probability to gravity
  • Int'l Joint Research / Invited
• [Presentation] Zeros of random analytic functions with dependent Gaussian coefficients (2021)
  • Author(s): 白井朋之
  • Organizer: 確率・ 統計・ 行列ワークショップ 彦根 2021
• [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
  • Invited
• [Presentation] Orthogonal theta functions associated with affine root systems and determinantal point processes (2021)
  • Author(s): Makoto Katori
  • Organizer: CIRM Conference - Modern Analysis Related to Root Systems with Applications
  • 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
• [Presentation] Hyperuniformity of the determinantal point processes associated with the Heisenberg group (2021)
  • 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」
  • Int'l Joint Research / Invited
• [Presentation] Duality of determinantal point processes (2020)
  • Author(s): Tomoyuki Shirai
  • Organizer: Workshop on "Random matrices, Determinantal point processes and Gaussian analytic functions"
• [Presentation] Limit theorems for determinantal point processes (2019)
  • Author(s): Tomoyuki Shirai
  • Organizer: International Conference on Mathematical Methods in Physics , Marrakesh, Morocco.
  • Int'l Joint Research / Invited
• [Presentation] Limit theorems for determinantal point processes (2019)
  • Author(s): Tomoyuki Shirai
  • Organizer: A Probability Conference on Random Matrices and Related Topics, KIAS, Seoul, Korea
  • Int'l Joint Research / Invited
• [Presentation] Limit theorems for persistence diagrams (2019)
  • Author(s): Tomoyuki Shirai
  • Organizer: Seminar at KTH Royal Institute of Technology, Sweden
  • Int'l Joint Research / Invited
• [Presentation] Partial isometries, duality, and determinantal point processes (2019)
  • Author(s): Makoto Katori
  • Organizer: Japanese-German Open Conference on Stochastic Analysis 2019, Sept.2-6, 2019, Fukuoka University, Japan
  • Int'l Joint Research / Invited
• [Presentation] Partial Isometries, Duality, and Determinantal Point Processes (2019)
  • Author(s): Makoto Katori
  • Organizer: Workshop on Random Matrices, Stochastic Geometry and Related Topics
  • Int'l Joint Research / Invited
• [Presentation] Systems of hard balls with long-range interactions (2019)
  • Author(s): Hideki Tanemura
  • Organizer: Workshop on Random Matrices, Stochastic Geometry and Related Topics
  • Int'l Joint Research / Invited
• [Presentation] Dynamic determinantal point processes (2019)
  • Author(s): Tomoyuki Shirai
  • Organizer: Ajou-Kyushu joint workshop on Industrial Mathematics
  • Int'l Joint Research / Invited
• [Presentation] Universality of determinantal point processes on Riemannian manifolds (2018)
  • Author(s): Tomoyuki Shirai
  • Organizer: RIMS Joint Research (Open): 17th International Symposium Stochastic Analysis on Large Scale Interacting Systems
  • Int'l Joint Research / Invited
• [Presentation] Limit theorems for determinantal point processes (2018)
  • Author(s): Tomoyuki Shirai
  • Organizer: エルゴード理論研究会
  • Invited
• [Remarks] https://imi.kyushu-u.ac.jp/~shirai/
• [Funded Workshop] Workshop on Probabilistic Methods in Statistical Mechanics of Random Media and Random Fields (2019)
• [Funded Workshop] Workshop on "Random matrices, stochastic geometry and related topics", NUS, Singapore. (Mar. 14th--16th, 2019) (2019)
• [Funded Workshop] International Conference on "Random matrices and their applications", (May. 21--25, 2018) (2018)