• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Study on random partitions and random matrices based on combinatorics and representation theory

Research Project

Project/Area Number 17K05281
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionKagoshima University

Principal Investigator

Matsumoto Sho  鹿児島大学, 理工学域理学系, 准教授 (60547553)

Project Period (FY) 2017-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2021: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2020: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Keywords対称群 / ヤング図形 / 既約指標 / ランダム行列 / Weingarten calculus / ランダムヤング図形 / ランダム分割 / 極限形 / 射影表現 / 組合せ論 / 表現論 / 確率論
Outline of Final Research Achievements

As a study on random matrices, especially on the Weingarten calculus, we have investigated the distribution of its partial traces for uniformly distributed random Hermitian matrices on tensor products. For random partitions, we have obtained Kerov polynomial representations and Stanley character formulas for the normalized spin irreducible characters of the symmetric group, and used them to obtain the law of large numbers and the central limit theorem for random shifted Young diagrams.

Academic Significance and Societal Importance of the Research Achievements

ランダム行列論はその名の通りランダムに振る舞う行列の集団を扱う分野で、数理物理学や量子情報理論を始め広い範囲に応用されている。また、その離散への類似物として、整数の分割をランダムに扱う、ランダム分割の研究がある。本研究はこれらについて具体的で視覚的に分かりやすい結果を得た。

Report

(7 results)
  • 2022 Annual Research Report   Final Research Report ( PDF )
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • Research Products

    (37 results)

All 2023 2022 2021 2020 2019 2018 2017 Other

All Int'l Joint Research (8 results) Journal Article (12 results) (of which Int'l Joint Research: 7 results,  Open Access: 9 results,  Peer Reviewed: 10 results) Presentation (14 results) (of which Int'l Joint Research: 6 results,  Invited: 3 results) Remarks (2 results) Funded Workshop (1 results)

  • [Int'l Joint Research] ニューヨーク大学(米国)

    • Related Report
      2022 Annual Research Report
  • [Int'l Joint Research] ポーランド科学アカデミー(ポーランド)

    • Related Report
      2022 Annual Research Report
  • [Int'l Joint Research] ポーランド科学アカデミー(ポーランド)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] カリフォルニア大学サンディエゴ校(米国)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] ポーランド科学アカデミー(ポーランド)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] ポーランド科学アカデミー(ポーランド)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] ポーランド科学アカデミー(ポーランド)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] カリフォルニア大学(米国)

    • Related Report
      2018 Research-status Report
  • [Journal Article] Moments of random quantum marginals via Weingarten calculus2023

    • Author(s)
      S. Matsumoto and C. McSwiggen
    • Journal Title

      International Mathematics Research Notices

      Volume: -

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] 長方形ヤング図形に対応する対称群指標の新しい表示2022

    • Author(s)
      松本 詔
    • Journal Title

      数理解析研究所講究録

      Volume: 2216 Pages: 64-81

    • Related Report
      2022 Annual Research Report
    • Open Access
  • [Journal Article] Symmetric group characters of almost square shape2022

    • Author(s)
      S. Matsumoto and P. Sniady
    • Journal Title

      Algebraic Combinatorics

      Volume: 5 Issue: 4 Pages: 771-784

    • DOI

      10.5802/alco.247

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] The Weingarten Calculus2022

    • Author(s)
      B. Collins Benoit, S. Matsumoto Sho, J. Novak
    • Journal Title

      Notices of the American Mathematical Society

      Volume: 69 Issue: 05 Pages: 734-745

    • DOI

      10.1090/noti2474

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] The Weingarten calculus2022

    • Author(s)
      Benoit Collins, Sho Matsumoto, Jonathan Novak
    • Journal Title

      Notices Of The American Mathematical Society

      Volume: -

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] 対称群のスピン表現に対するStanley指標公式2020

    • Author(s)
      松本詔
    • Journal Title

      数理解析研究所講究録

      Volume: 2161 Pages: 58-72

    • Related Report
      2020 Research-status Report
    • Open Access
  • [Journal Article] Linear versus spin: representation theory of the symmetric groups2020

    • Author(s)
      Sho Matsumoto, Piotr Sniady
    • Journal Title

      Algebraic Combinatorics

      Volume: 3 Issue: 1 Pages: 249-280

    • DOI

      10.5802/alco.92

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Random strict partitions and random shifted tableaux2020

    • Author(s)
      Sho Matsumoto, Piotr Sniady
    • Journal Title

      Selecta Mathematica

      Volume: 26

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] A Spin Analogue of Kerov Polynomials2018

    • Author(s)
      Sho Matsumoto
    • Journal Title

      Symmetry, Integrability and Geometry: Methods and Applications

      Volume: 14 Pages: 53-53

    • DOI

      10.3842/sigma.2018.053

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] A moment method for invariant ensembles2018

    • Author(s)
      Sho Matsumoto and Jonathan Novak
    • Journal Title

      Electronic Research Announcements

      Volume: 25 Issue: 0 Pages: 60-71

    • DOI

      10.3934/era.2018.25.007

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Polynomiality of shifted Plancherel averages and content evaluations2017

    • Author(s)
      Sho Matsumoto
    • Journal Title

      Annales Mathematiques Blaise Pascal

      Volume: 24 Issue: 1 Pages: 55-82

    • DOI

      10.5802/ambp.364

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Weingarten calculus via orthogonality relations: new applications2017

    • Author(s)
      Benoit Collins and Sho Matsumoto
    • Journal Title

      ALEA, Lat. Am. J. Probab. Math. Stat.

      Volume: 14 Pages: 631-656

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Presentation] Moments of partial traces for random Hermitian matrices and Weingarten calculus2023

    • Author(s)
      Sho Matsumoto
    • Organizer
      Seminar Bielefeld - Melbourne Random Matrices
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 対称群の正規化指標に関する幾つかの結果とスピン類似2022

    • Author(s)
      松本 詔
    • Organizer
      Non-Commutative Probability and Related Topics 2022
    • Related Report
      2022 Annual Research Report
  • [Presentation] 長方形ヤング図形に対応する対称群指標の新しい表示2021

    • Author(s)
      松本詔
    • Organizer
      RIMS共同研究(公開型)「組合せ論的表現論および関連分野との連携」
    • Related Report
      2021 Research-status Report
  • [Presentation] ほぼ正方形のヤング図形に対応する対称群の正規化指標2021

    • Author(s)
      松本詔
    • Organizer
      第2回 分布族・離散集合の幾何学とその周辺
    • Related Report
      2020 Research-status Report
  • [Presentation] 対称群のスピン指標のStanley指標公式2020

    • Author(s)
      松本詔
    • Organizer
      JCCA2020-DMIA2020-SGT9
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] Kerov多項式とStanley指標公式2019

    • Author(s)
      松本詔
    • Organizer
      可換確率論と非可換確率論の相互作用準備会
    • Related Report
      2019 Research-status Report
  • [Presentation] Kerov polynomials and Stanley formulas for spin symmetric groups2019

    • Author(s)
      Sho Matsumoto
    • Organizer
      Interactions between commutative and non-commutative probability
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] 対称群のStanley指標公式とmapの数え上げ2019

    • Author(s)
      松本詔
    • Organizer
      Study Meeting on Graph and Curvature
    • Related Report
      2019 Research-status Report
  • [Presentation] 対称群のスピン表現に対するStanley指標公式2019

    • Author(s)
      松本詔
    • Organizer
      RIMS共同研究(公開型)「表現論とその組合せ的側面」
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Weingarten calculus for random matrices associated with the compact symmetric space of class D III2019

    • Author(s)
      Sho Matsumoto
    • Organizer
      Workshop on "Random Matrices and Related Topics"
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] Weingarten calculus and counting paths on Weingarten graphs2018

    • Author(s)
      Sho Matsumoto
    • Organizer
      Random matrices and their applications
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 直交群の Weingarten calculus と Weingarten グラフ2018

    • Author(s)
      松本詔
    • Organizer
      2018年度(第57回)実函数論・函数解析学合同シンポジウム
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] 対称群のスピン表現に対するKerov多項式2018

    • Author(s)
      松本詔
    • Organizer
      RIMS共同研究(公開型)「組合せ的表現論の諸相」
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] Weingarten calculus for Haar distributed matrices and Wishart matrices2017

    • Author(s)
      松本詔
    • Organizer
      確率・統計・行列ワークショップ松本2017
    • Related Report
      2017 Research-status Report
  • [Remarks] 松本詔のホームページ

    • URL

      https://sites.google.com/site/shomatsumotomath1/

    • Related Report
      2022 Annual Research Report
  • [Remarks] 松本詔のホームページ

    • URL

      https://sites.google.com/site/shomatsumotomath1/home

    • Related Report
      2021 Research-status Report 2020 Research-status Report 2019 Research-status Report 2018 Research-status Report 2017 Research-status Report
  • [Funded Workshop] Workshop on "Random Matrices and Related Topics"2019

    • Related Report
      2018 Research-status Report

URL: 

Published: 2017-04-28   Modified: 2024-01-30  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi