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Affiliation |
Faculty of Science Department of Mathematics and Infomation Science |
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Title |
特任教授 |
Yoshida Hiroaki
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Degree 【 display / non-display 】
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工学博士 ( 1988.12 大阪大学 )
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工学修士 ( 1985.03 大阪大学 )
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理学士 ( 1983.03 大阪大学 )
Research Areas 【 display / non-display 】
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Natural Science / Applied mathematics and statistics / 統計的データ解析、ランダム行列
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Natural Science / Basic analysis / 関数解析, 作用素環, 非可換確率論
From School 【 display / non-display 】
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Osaka University Faculty of Science Department of Mathematics Graduated
1979.04 - 1983.03
From Graduate School 【 display / non-display 】
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大阪大学大学院 基礎工学研究科 前期課程 数理系専攻 Master's Course Completed
1983.04 - 1985.03
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大阪大学大学院 基礎工学研究科 後期課程 数理系専攻 Doctor's Course Completed
1985.04 - 1988.12
Employment Record in Research 【 display / non-display 】
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城西大学 理学部 情報数理学科 理学部 特任教授
2025.04
External Career 【 display / non-display 】
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Ochanomizu University Professor
2015.04 - 2025.03
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Ochanomizu University Graduate School of Humanities and Sciences Professor
2007.04 - 2015.03
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Ochanomizu University Faculty of Science Professor
2004.04 - 2007.03
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文部省 短期在外研究員 カリフォルニア大学バークレー校 客員研究員
1998.03 - 1998.05
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Ochanomizu University Faculty of Science Associate Professor (as old post name)
1993.04 - 2004.03
Professional Memberships 【 display / non-display 】
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日本数学会
1985.03
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日本統計学会
1989.03
Papers 【 display / non-display 】
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Two parameterized deformed Poisson type operator and the combinatorial moment formula Reviewed
Nobuhiro Asai, Hiroaki Yoshida
Journal of Mathematical Analysis and Applications 543 ( 1 ) 128888 2025.03
Language：English Publishing type：Research paper (scientific journal) Publisher：Elsevier BV
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Meixner random variables and their quantum operators Reviewed
Nobuaki Obata, Aurel I. Stan, Hiroaki Yoshida
Infinite Dimensional Analysis, Quantum Probability and Related Topics 27 2024.06
Language：English Publishing type：Research paper (scientific journal) Publisher：World Scientific Pub Co Pte Ltd
In this paper, we find the position–momentum decomposition of the quantum operators of the classic Meixner random variables. The position–momentum decomposition involves translation operators, which are used to give a new characterization of the Meixner random variables.
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Combinatorial aspects of weighted free Poisson random variables Reviewed
Nobuhiro Asai, Hiroaki Yoshida
Infinite Dimensional Analysis, Quantum Probability and Related Topics 27 ( 03 ) 2024.02
Language：English Publishing type：Research paper (scientific journal) Publisher：World Scientific Pub Co Pte Ltd
This paper will be devoted to the study of weighted (deformed) free Poisson random variables from the viewpoint of orthogonal polynomials and statistics of non-crossing partitions. A family of weighted (deformed) free Poisson random variables will be defined in a sense by the sum of weighted (deformed) free creation, annihilation, scalar, and intermediate operators with certain parameters on a weighted (deformed) free Fock space together with the vacuum expectation. We shall provide a combinatorial moment formula of non-commutative Poisson random variables. This formula gives us a very nice combinatorial interpretation to two parameters of weights. One can see that the deformation treated in this paper interpolates free and boolean Poisson random variables, their distributions and moments, and yields some conditionally free Poisson distribution by taking limit of the parameter.
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Deformed Gaussian operators on weighted q-Fock spaces Reviewed
Nobuhiro Asai, Hiroaki Yoshida
Journal of Stochastic Analysis 1 ( 4 ) 06 - 8pages 2020.12
DOI： 10.31390/josa.1.4.06
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Remarks on a Free Analogue of the Beta Prime Distribution Reviewed
YOSHIDA Hiroaki
J. Theor. Probab. 33 ( 3 ) 1363 - 1400 2020.06
Language：English Publishing type：Research paper (scientific journal)
Presentations 【 display / non-display 】
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On combinatorial moment formula of deformed Poisson random variables Invited
Hiroaki Yoshida
Non-commutative probability, random matrices, and Lévy processes 2025 2025.03
Event date： 2025.03
Language：English Presentation type：Oral presentation (invited, special)
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An application of fluctuation moments of random matrices to statistical data analysis Invited
Hiroaki Yoshida
Random Matrices and Applications, Kyoto Univ. 2023.06
Event date： 2023.06
Language：English Presentation type：Oral presentation (invited, special)
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The free beta prime distribution and related free analogues Invited International conference
YOSHIDA Hiroaki
Interactions between commutative and non-commutative probability 2019.08 The JSPS Program of Bilateral Joint Seminars (JP--FR)
Event date： 2019.08
Language：English
Venue：Kyoto, Japan
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The free analogue of the beta prime distribution and its properties Invited
Hiroaki Yoshida
Non-commutative probability and related fields 2018.11 Hokkaido Univ.
Event date： 2018.11
Language：English
Venue：Sapporo, Japan
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自由確率論における Fokker-Planck 方程式とエントロピー消散 Invited
YOSHIDA Hiroaki
第57回実函数論・函数解析学合同シンポジウム 2018.09
Event date： 2018.09
Language：Japanese
Scientific Research Funds Acquisition Results 【 display / non-display 】
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非可換確率空間における分布特性量の変形と独立性の対応
Grant number：20K03649 2020.04 - 2025.03
日本学術振興会 科学研究費助成事業 基盤研究(C)
吉田 裕亮
Grant amount：\4550000 （ Direct Cost: \3500000 、 Indirect Cost：\1050000 ）
本研究課題では, 非可換確率空間における独立性の概念を Fisher 情報量やエントロピーなどの分布特性量の視点から捉える新たな手法の開発を目指している. 本研究課題は独立性の変形と分布特性量を変形の対応に着目して, まず自由独立性と通常独立性を補間する q-変形独立性に関して, 特性量の変形が如何に振舞うかを Meixner 分布族をテスト分布として具体的に調べることから開始された.
令和 3 年度は, これまでの q-変形に, さらに変形パラメータを加えた 2 係数 (q, s)－変形 Fock 空間上の変形 Poisson 分布に関する研究を愛知教育大の淺井氏と共に行ない, 研究成果を学術雑誌に投稿を行った. この (q, s)－変形 Fock 空間の生成・消滅作用素の交換関係で特徴的なことは恒等作用素が s-変形することで qs-交換関係が構成され, 対応する変形 Poisson 作用素が q-個数作用素と s-変形恒等作用素を用いて構成されることになる. さらにこの (q,s)-Fock 空間上の作用素構成法により同変形 Poisson 分布の高次モーメントの組合せ論的表示も同時に発見している.
また本研究課題と関連する非可換確率論分野の研究として, 自由独立性の下での古典ベータ分布族の自由類似に関連して, この自由類似と自由群の表現論との潜在関係の解明への鍵が名古屋大の山上氏との研究討議において発見された. これに関しては, 現在, 有限階数摂動法を用いて精査し, 学術論文への投稿を目指して取り纏めを行っている.
加えて 令和 3 年 11月に名古屋大学においてハイブリッド開催された研究集会「非可換確率論とその関連分野 2021」にはオーガナイザの一人として参画し, 国内の関連研究者の最新の研究動向の調査も行った. -
Deformation of Fisher information and entropy in non-commutative probability spaces
Grant number：26400112 2014.04 - 2020.03
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
Yoshida Hiroaki
Authorship：Principal investigator Grant type：Competitive
In this study, we have investigated quantum deformed entropy and Fisher information in non-commutative probability space. Using the correspondence between quantum deformed independence and potential functions, the free analogue of the beta prime distribution and its related distributions, F-distribution and t-distribution, have been introduced to the theory of free probability related to the score function of Fisher information.
Furthermore, we have succeeded to give an application of random matrices to the statistical data analysis, which allows us to expect further applications of non-commutative probability theory to other fields. -
非可換確率空間における確率分布の変形に関する研究
Grant number：21540213 2009.04 - 2014.03
日本学術振興会 科学研究費補助金 基盤研究（Ｃ）
吉田 裕亮
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Deformations of independence on non-commutative probability spaces and deformed Fock spaces
Grant number：17540190 2005.04 - 2009.04
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
YOSHIDA Hiroaki, YANO Yuko
Authorship：Principal investigator Grant type：Competitive
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Deformation of independences in non-commutative probability spaces
Grant number：14540201 2002.04 - 2005.03
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
YOSHIDA Hiroaki, KASAHARA Yuji
Authorship：Principal investigator Grant type：Competitive
In usual probability space, if the pair of an algebra of bounded random variable on it and an expectation map then we can reconstruct the original probability space from such a pair of an algebra and an expectation map. The above algebra is commutative, hence, the usual probability space can be associated with a commutative algebra. Non-commutative probability space can be obtained by malting the algebra be non-commutative. Sometime such a procedure would be called quantization. Although the independence on usual probability spaces can be extended to a non-commutative probability space, it will require that independent random variables should be commutative. Unfortunately, this extension will not reflect well non-commutativity because the usual independence is based on tensor product. Voiculescu introduced the free independence which is based on free products and reflects well non-commutativity.
If we are restricted that the independence should give the rule of calculation for mixed moments then only three kinds of independence (usual, free, and Boolean) are allowed in non-commutative probability space under some axioms. This is most explicit formalization of independence in non-commutative probability space. In general, independences should determine convolutions, and convolutions would give the moments-cumulants formulae. Standing this point of view, we can consider a more implicit deformed independence by deformations of moments-cumulants formula.
In this project, we have adopted this procedure, that is, we have considered the deformation of independence by making deformations of moments-cumulants formulae. We have made several deformed free convolution, which interpolate free and Boolean convolutions. For the s-free and the r-free deformations, we investigated the corresponding Gaussian and Poisson random variables, especially on the s-free case, we have constructed the s-free Fock space (one of deformations of full Fock space) and gave the s-free Gaussian and the s-free Poisson random variables by the annihilation and the creation operators. Furthermore, we have extended the q-deformation, which is well known example that interpolates usual (the Boson Fock space) and Boolean (the Fermionic Fock space) convolutions, to 2-parameters cases. We call such a deformation the generalized q-deformation. As the generalized q-deformation, the (q,t) and the (q,s) deformations have been investigated and corresponding set partition statistics are also studied. Much more general deformed free convolution, the Delta-deformation, was introduced by Bozejko. We also succeeded to construct the weight function on non-crossing partitions for any given Delta convolution, which suggests us some kinds of new set partition statistics on non-crossing partitions.