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

Research on Random Matrices Motivated by Free Probability

Research Project

Project/Area Number 24740057
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionAichi University of Education

Principal Investigator

SAKUMA Noriyoshi  愛知教育大学, 教育学部, 講師 (70610187)

Project Period (FY) 2012-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords自由確率論 / 無限分解可能分布 / 国際情報交換 / メキシコ / ポーランド / フランス / ランダム行列 / レヴィ過程 / 国際研究者交流
Outline of Final Research Achievements

We study Random Matrix motivated by free probability. In this project, limiting spectral distributions of large random matricies were studied from free probability. In particular, we studied random matrix models with dependent entries and we proved its limiting distributions are the compound free Poisson distributions. We also computed fluctuations by "second order freeness".
On the other hand, we studied time evolution of distributions of free infinitely divisible distributions which is important to study time evolution of Random matrix valued processes.
We wrote some papers related to this results. I gave talks related to these results more than 10 times.

Report

(4 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (15 results)

All 2015 2014 2013 2012 Other

All Journal Article (6 results) (of which Peer Reviewed: 5 results,  Acknowledgement Compliant: 2 results) Presentation (8 results) (of which Invited: 3 results) Remarks (1 results)

  • [Journal Article] Unimodality of Boolean and monotone stable distributions2015

    • Author(s)
      Takahiro Hasebe and Noriyoshi Sakuma
    • Journal Title

      Demonstr. Math.

      Volume: 未定

    • NAID

      120006734191

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Generalized gamma convolutions と Markov 変換2015

    • Author(s)
      Octavio Arizmendi and Noriyoshi Sakuma
    • Journal Title

      統計数理研究所共同研究リポート350, 無限分解可能過程に関連する諸問題 (19)

      Volume: 350 Pages: 96-102

    • Related Report
      2014 Annual Research Report
    • Acknowledgement Compliant
  • [Journal Article] On the law of free subordinators.2013

    • Author(s)
      Arizmendi, Octavio; Hasebe, Takahiro; Sakuma, Noriyoshi
    • Journal Title

      Am. J. Probab. Math. Stat.

      Volume: 10

    • NAID

      120006734186

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Random matrices by MA models and compound free Poisson laws.2013

    • Author(s)
      Hasegawa, Ayako; Sakuma, Noriyoshi; Yoshida, Hiroaki
    • Journal Title

      Probability and Mathematical Statistics

      Volume: 33

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] New limit theorems related to free multiplicative convolution2013

    • Author(s)
      N. Sakuma and H. Yoshida
    • Journal Title

      Studia Math.

      Volume: 未定

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Distributions of exponential integrals of independent increment processes related to generalized gamma convolutions2012

    • Author(s)
      A. Behme, M. Maejima, M. Matsui and N. Sakuma
    • Journal Title

      Bernoulli

      Volume: 18 Pages: 1172-1187

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] Generalized gamma convolutions と Markov 変換2014

    • Author(s)
      佐久間紀佳
    • Organizer
      共同研究集会「無限分解可能過程に関連する諸問題」
    • Place of Presentation
      統計数理研究所(東京都)
    • Year and Date
      2014-11-29
    • Related Report
      2014 Annual Research Report
  • [Presentation] On Marchenko-Pastur limit of random matrices with dependent entries2014

    • Author(s)
      Noriyoshi Sakuma
    • Organizer
      CIMAT probability seminar
    • Place of Presentation
      メキシコ, CIMAT
    • Year and Date
      2014-10-06
    • Related Report
      2014 Annual Research Report
  • [Presentation] On Marchenko-Pastur limit of random matrices with dependent entries2014

    • Author(s)
      Noriyoshi Sakuma
    • Organizer
      16th WORKSHOP: NON-COMMUTATIVE HARMONIC ANALYSIS
    • Place of Presentation
      Bedlewo, Poland
    • Year and Date
      2014-07-07
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 自由確率論における非減少レヴィ過程の分布について2012

    • Author(s)
      佐久間紀佳
    • Organizer
      確率論シンポジウム
    • Place of Presentation
      京都大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Variance mixture and subordinator in free probability2012

    • Author(s)
      佐久間紀佳
    • Organizer
      確率解析とその周辺
    • Place of Presentation
      名古屋大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Free infinitely divisible distributions from a point of view of subordinators and mixtures

    • Author(s)
      Noriyoshi Sakuma
    • Organizer
      7th International Conference on Levy Processes
    • Place of Presentation
      Wroclaw, Poland
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] 成分間に従属性があるランダム行列の極限スペクトル分布について

    • Author(s)
      佐久間紀佳
    • Organizer
      無限分解可能過程に関連する諸問題
    • Place of Presentation
      統計数理研究所
    • Related Report
      2013 Research-status Report
  • [Presentation] MAモデルに基づくランダム行列と複合自由ポアソン分布

    • Author(s)
      佐久間紀佳
    • Organizer
      九州確率論セミナー
    • Place of Presentation
      九州大学
    • Related Report
      2013 Research-status Report
  • [Remarks] Noriyoshi Sakuma

    • URL

      http://auemath.aichi-edu.ac.jp/~sakuma/

    • Related Report
      2014 Annual Research Report

URL: 

Published: 2013-05-31   Modified: 2019-07-29  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi