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On averages for symmetric functions under Plancherel probability measures

Research Project

Project/Area Number 22740060
Research Category

Grant-in-Aid for Young Scientists (B)

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

Principal Investigator

MATSUMOTO Sho  名古屋大学, 多元数理科学研究科, 助教 (60547553)

Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords代数学 / 解析学 / ランダム行列 / 対称関数 / 確率論 / 対称群 / 行列積分 / 組合せ論 / 関数解析
Research Abstract

The theme of our research is to study about connections between Plancherel measures on Young diagrams and random matrix theory. We have established the method for computations of averages of matrix entries, which are derived from random unitary matrices, random orthogonal matrices, inverse of real Wishart matrices, COE matrices, and so on. Moreover, we have given some combinatorial and representation-theoretic interpretations for them via Plancherel measures.

Report

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

    (34 results)

All 2013 2012 2011 2010 Other

All Journal Article (13 results) (of which Peer Reviewed: 12 results) Presentation (18 results) Remarks (3 results)

  • [Journal Article] Jucys-Murphy elements and unitary matrix integrals2013

    • Author(s)
      S. Matsumoto and J. Novak
    • Journal Title

      International Mathematics Research Notice

      Volume: no.2 Pages: 362-397

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Jucys-Murphy elements and unitary matrix integrals2013

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

      International Mathematics Research Notices

      Volume: 2013 Issue: 2 Pages: 362-397

    • DOI

      10.1093/imrn/rnr267

    • Related Report
      2012 Annual Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Moments of a single entry of circular orthogonal ensembles and Weingarten calculus2013

    • Author(s)
      Sho Matsumoto
    • Journal Title

      Letters in Mathematical Physics

      Volume: 103 Issue: 2 Pages: 113-130

    • DOI

      10.1007/s11005-012-0587-0

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Weingarten calculus for matrix ensembles associated with compact symmetric spaces2013

    • Author(s)
      Sho Matsumoto
    • Journal Title

      Random Matrices: Theory and Applications

      Volume: 未定 Issue: 02 Pages: 1350001-1350001

    • DOI

      10.1142/s2010326313500019

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] General moments of the inverse real Wishart distribution and orthogonal Weingarten functions2012

    • Author(s)
      S. Matsumoto
    • Journal Title

      Journal of Theoretical Probability

      Volume: 25、no.3 Pages: 798-822

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] General moments of the inverse real Wishart distribution and orthogonal Weingarten functions2012

    • Author(s)
      Sho Matsumoto
    • Journal Title

      Journal of Theoretical Probability

      Volume: 25 Issue: 3 Pages: 798-822

    • DOI

      10.1007/s10959-011-0340-0

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] General moments of matrix elements from circular orthogonal ensembles2012

    • Author(s)
      Sho Matsumoo
    • Journal Title

      Random Matrices: Theory and Applications

      Volume: 1 Issue: 03 Pages: 125005-125005

    • DOI

      10.1142/s2010326312500050

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 直交群のWeingarten関数と帯多項式2012

    • Author(s)
      松本 詔
    • Journal Title

      数理解析研究所講究録 別冊

      Volume: B36

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Jucys-Murphy elements, orthogonal matrix integrals, and Jack measures2011

    • Author(s)
      S. Matsumoto
    • Journal Title

      The Ramanujan Journal

      Volume: 26、no.1 Pages: 69-7

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Jucys-Murphy elements, orthogonal matrix integrals, and Jack measures2011

    • Author(s)
      S.Matsumoto
    • Journal Title

      The Ramanujan Journal

      Volume: 26 Issue: 1 Pages: 69-107

    • DOI

      10.1007/s11139-011-9317-y

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Jucys-Murphy元を変数とする対称関数2011

    • Author(s)
      松本詔
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1770 Pages: 35-51

    • Related Report
      2011 Annual Research Report
  • [Journal Article] プランシェレル測度のジャック版の極限定理2010

    • Author(s)
      松本詔
    • Journal Title

      数理解析研究所講究録別冊

      Volume: B20 Pages: 39-55

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] General moments of the inverse real Wishart distribution and Weingarten functions

    • Author(s)
      Sho Matsumoto
    • Journal Title

      Jourmal of Theoretical Probability

      Volume: (採録決定 未定)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] Zeros of a Gaussian power series and Pfaffians2012

    • Author(s)
      S. Matsumoto
    • Organizer
      Workshop 「 Algebraic Combinatorics related to Young diagrams and Statistical Physics」
    • Place of Presentation
      京都大学、国際高等研究所
    • Year and Date
      2012-08-07
    • Related Report
      2012 Final Research Report
  • [Presentation] Moments of matrix elements from the orthogonal group and COE2012

    • Author(s)
      松本詔
    • Organizer
      7th Algebra-Analysis-Geometry Seminar 2012
    • Place of Presentation
      鹿児島大学
    • Year and Date
      2012-02-17
    • Related Report
      2011 Annual Research Report
  • [Presentation] Moments of matrix entries from the circular orthogonal ensemble2012

    • Author(s)
      Sho Matsumoto
    • Organizer
      Workshop "Probability and asymptotic analysis II"
    • Place of Presentation
      名古屋大学
    • Related Report
      2012 Annual Research Report
  • [Presentation] Pfaffian formulas related to Gaussian power series2012

    • Author(s)
      Sho Matsumoto
    • Organizer
      Workshop "Forum on Probability, Statistics, Algebra and Combinatorics "
    • Place of Presentation
      名古屋大学
    • Related Report
      2012 Annual Research Report
  • [Presentation] Zeros of a Gaussian power series and Pfaffian2012

    • Author(s)
      Sho Matsumoto
    • Organizer
      Workshop "Algebraic Combinatorics related to Young diagrams and Statistical Physics"
    • Place of Presentation
      京都大学
    • Related Report
      2012 Annual Research Report
  • [Presentation] ガウス型べき級数の実零点過程の相関関数とパフィアン2012

    • Author(s)
      松本詔, 白井朋之
    • Organizer
      日本数学会2012年度秋季総合分科会, 統計数学分科会
    • Place of Presentation
      九州大学
    • Related Report
      2012 Annual Research Report
  • [Presentation] Pfaffian expressions for correlation functions of zeros of a Gaussian power series2012

    • Author(s)
      松本 詔
    • Organizer
      研究集会「確率解析とその周辺」(確率解析シンポジウム)
    • Place of Presentation
      名古屋大学
    • Related Report
      2012 Annual Research Report
  • [Presentation] Zeros of Gaussian power series and Pfaffians2012

    • Author(s)
      松本 詔
    • Organizer
      研究集会「Zetas and Limit Laws in OKINAWA 2012」
    • Place of Presentation
      沖縄県宜野湾市
    • Related Report
      2012 Annual Research Report
  • [Presentation] COE 行列成分に関するモーメントの計算法2011

    • Author(s)
      松本詔
    • Organizer
      確率論シンポジウム
    • Place of Presentation
      関西大学
    • Year and Date
      2011-12-21
    • Related Report
      2012 Final Research Report
  • [Presentation] COE行列の行列成分に関するモーメントの計算法2011

    • Author(s)
      松本詔
    • Organizer
      確率論シンポジウム
    • Place of Presentation
      関西大学
    • Year and Date
      2011-12-21
    • Related Report
      2011 Annual Research Report
  • [Presentation] On Moments o entries of a COE matrix2011

    • Author(s)
      松本詔
    • Organizer
      Workshop "Integrable systems, random matrices, algebraic geometry and geometric invariants"
    • Place of Presentation
      京都大学
    • Year and Date
      2011-10-20
    • Related Report
      2011 Annual Research Report
  • [Presentation] COEランダム行列の行列成分モーメントの計算法2011

    • Author(s)
      松本詔
    • Organizer
      研究集会「表現論がつなぐ数学の展望」
    • Place of Presentation
      ホテルサンルート名古屋駅前店
    • Year and Date
      2011-08-29
    • Related Report
      2011 Annual Research Report
  • [Presentation] Jucys-Murphy元を変数とする対称関数2011

    • Author(s)
      松本詔
    • Organizer
      RIMS研究集会「表現論と調和解析における諸問題」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2011-06-28
    • Related Report
      2011 Annual Research Report
  • [Presentation] Unitary matrix integrals and enumerations of permutations2010

    • Author(s)
      S. Matsumoto
    • Organizer
      Workshop「Integrable Systems, Random Matrices, Algebraic Geometry and Geometric Invariants」
    • Place of Presentation
      京都大学
    • Year and Date
      2010-12-15
    • Related Report
      2012 Final Research Report
  • [Presentation] Unitary matrix integrals and enumerations of permutations2010

    • Author(s)
      Sho Matsumoto
    • Organizer
      Workshop 'Integrable Systems, Random Matrices, Algebraic Geometry and Geometric Invariants'
    • Place of Presentation
      京都大学
    • Year and Date
      2010-12-15
    • Related Report
      2010 Annual Research Report
  • [Presentation] Unitary matrix integrals and enumerations of permutations2010

    • Author(s)
      Sho Matsumoto
    • Organizer
      Functions in Number Theory and Their Probabilistic Aspect
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-12-13
    • Related Report
      2010 Annual Research Report
  • [Presentation] Real Wishart Matrices and Haar-distributed orthogonal matrices2010

    • Author(s)
      Sho Matsumoto
    • Organizer
      34th Conference on Stochastic Processes and Their Applications
    • Place of Presentation
      千里ライフサイエンスセンター(大阪府)
    • Year and Date
      2010-09-06
    • Related Report
      2010 Annual Research Report
  • [Presentation] ガウス型べき級数とパフィアンの恒等式

    • Author(s)
      松本 詔
    • Organizer
      研究集会「表現論から見える数学の諸相」
    • Place of Presentation
      沖縄県那覇市
    • Related Report
      2012 Annual Research Report
  • [Remarks]

    • URL

      http://www.math.nagoya-u.ac.jp/sho-matsumoto/index.html

    • Related Report
      2012 Final Research Report
  • [Remarks] 松本 詔 web page

    • URL

      http://www.math.nagoya-u.ac.jp/~sho-matsumoto/index.html

    • Related Report
      2012 Annual Research Report
  • [Remarks]

    • URL

      http://www.math.nagoya-u.ac.jp/~sho-matsumoto/index.html

    • Related Report
      2011 Annual Research Report

URL: 

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

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