Deformations of probability distributions on non-commutative probability spaces

• Project/Area Number: 21540213
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Global analysis
• Research Institution: Ochanomizu University
• Principal Investigator: YOSHIDA Hiroaki お茶の水女子大学, 大学院人間文化創成科学研究科, 教授 (10220667)
• Project Period (FY): 2009-04-01 – 2014-03-31
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); 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: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: 関数解析学 / 作用素環論 / 非可換確率論 / 変形分布論 / 量子情報理論 / 量子変形分布 / 変形分布 / 分割統計

Research Abstract

In this project, a deformed family of the classical Meixner distributions was considered as one of important examples for quantum deformations, and non-commutative random variables having these deformed Meixner distributions were constructed on the deformed Fock space by using the corresponding deformed annihilation and creation operators.
We have also investigated the fundamental theories on quantum deformed entropy and Fisher information. Especially, in the case of free probability, we have given another proofs for several inequalities on the relative free entropy and the free Fisher information based on the free diffusion processes.

Research Products

• [Journal Article] Random Matrices by MA models and compound free Poisson laws (2013)
  • Author(s): Ayako Hasegawa, Noriyoshi Sakuma and Hiroaki Yoshida
  • Journal Title: Probab. Math. Statist Volume: 33 Pages: 243-254
  • URL: http://www.math.uni.wroc.pl/~pms/files/33.2/Article/33.2.6.pdf
  • Peer Reviewed
• [Journal Article] New limit theorems related to free multiplicative convolution (2013)
  • Author(s): Noriyoshi Sakuma and Hiroaki Yoshida
  • Journal Title: Studia Math Volume: 214 Issue: 3 Pages: 251-264
  • DOI: 10.4064/sm214-3-4
  • Peer Reviewed
• [Journal Article] Random Matrices by MA models and compound free Poisson laws (2013)
  • Author(s): Ayako Hasegawa, Noriyoshi Sakuma, Hiroaki Yoshida
  • Journal Title: Probab. Math. Statist. Volume: 33 Pages: 243-254
  • Peer Reviewed
• [Journal Article] An integral representation of the relative entropy (2012)
  • Author(s): Miku Hirata, Aya Nemoto, and Hiroaki Yoshida
  • Journal Title: Entropy Volume: 14 Issue: 8 Pages: 1469-1477
  • DOI: 10.3390/e14081469
  • Peer Reviewed
• [Journal Article] The q-Meixner distributions associated with a q-deformed symmetric Fock space (2011)
  • Author(s): Hiroaki Yoshida
  • Journal Title: J. Phys. A : Math. Theor Volume: 44, 165306 Issue: 16 Pages: 8-8
  • DOI: 10.1088/1751-8113/44/16/165306
  • Peer Reviewed
• [Journal Article] Remarks on the free relative entropy and the free Fisher information distance (2010)
  • Author(s): Hiroaki Yoshida
  • Journal Title: Infin.Dim. Anal. Quantum. Probab. Relat. Top Volume: 13 Issue: 02 Pages: 243-255
  • DOI: 10.1142/s0219025710004048
  • Peer Reviewed
• [Journal Article] Remarks on the free relative entropy and free Fisher information distance (2010)
  • Author(s): Hiroaki YOOSHIDA
  • Journal Title: Infinite Dimensional Analysis, Quantum Probability and Related Topics Volume: 13 Pages: 243-255
  • Peer Reviewed
• [Presentation] The free logarithmic Sobolev and transportation cost inequalities by time integration (2013)
  • Author(s): Hiroaki Yoshida
  • Organizer: The 8th Jikji Workshop on Infinite Dimensional Analysis and Quantum Probability
  • Place of Presentation: National Iinstitute for Mathematical Sciences, Daejeon, Korea
  • Year and Date: 2013-08-20
  • Invited
• [Presentation] Applications of dissipation formulas of the relative free entropy (2013)
  • Author(s): Hiroaki Yoshida
  • Organizer: International Workshop on Noncommutative Analysis and its Future Prospects
  • Place of Presentation: Hokkaido University, Sapporo, Japan
  • Year and Date: 2013-08-06
  • Invited
• [Presentation] Applications of the time derivative of the Wasserstein distance and the free entropy dissipation (2013)
  • Author(s): Hiroaki Yoshida
  • Organizer: Workshop on Analytic, Stochastic, and Operator Algebraic Aspects of Noncommutative Distributions and Free Probability
  • Place of Presentation: Fields Institute, Univ. Toronto, Toronto, Canada
  • Year and Date: 2013-07-23
  • Invited
• [Presentation] On derivation of the relative free entropy and the Talagrand's inequality for the semi-circle law" (2012)
  • Author(s): Hiroaki Yoshida
  • Organizer: The 15th Workshop: Non-Commutative Harmonic Analysis
  • Place of Presentation: The Mathematical Research and Conference Center Banach Institute, Bedlewo, Poland
  • Year and Date: 2012-09-26
  • Invited
• [Presentation] Integral representa- tions of the relative free entropy associated with semicircular gradi- nts (2011)
  • Author(s): Hiroaki Yoshida
  • Organizer: The 14th Workshop Non-Commutative Harmonic Analysis
  • Place of Presentation: The Mathematical Research and Conference Center, Banach Institute, Bedlewo, Poland
  • Year and Date: 2011-09-27
  • Invited
• [Presentation] The free Poisson limit by the free Fisher information distance (2011)
  • Author(s): Hiroaki Yoshida
  • Organizer: Sapporo Workshop on Non-Commutative Analysis and Applica -tions to Complex Phenomena
  • Place of Presentation: Hokkaido Uniiversity, Sapporo, Japan
  • Year and Date: 2011-09-01
  • Invited
• [Presentation] On self-adjoint q-Meixner operators (2011)
  • Author(s): Hiroaki YOSHIDA
  • Organizer: The 6th Jikji-Workshop : Innite Dimensional Analysis and Quantum Probability
  • Place of Presentation: 韓国国家数理科学研究所大田・大韓民国
  • Year and Date: 2011-01-10
• [Presentation] q-Fock空間上のq-Meixner型自己共役作用素 (2010)
  • Author(s): 吉田裕亮
  • Organizer: 研究集会「独立性と従属性の数理」
  • Place of Presentation: 京都大学数理解析研究所京都・日本
  • Year and Date: 2010-12-22
• [Presentation] On the free Fisher information distance and the logarithmic Sobolev inequality (2010)
  • Author(s): Hiroaki Yoshida
  • Organizer: The 13th Workshop NonCommutative Harmonic Analysis
  • Place of Presentation: The Mathematical Research and Conference Center Banach Institute,Bedlewo, Poland
  • Year and Date: 2010-07-14
  • Invited
• [Presentation] On the free Fisher information distance and the logarithmic Sobolev inequality (2010)
  • Author(s): Hiroaki YOSHIDA
  • Organizer: 13th WORKSHOP : NON-COMMUTATIVE HARMONIC ANALYSIS
  • Place of Presentation: ポーランド科学アカデミーポズナン・ポーランド
  • Year and Date: 2010-07-14
• [Presentation] On self-adjoint q-Meixner operators (2010)
  • Author(s): Hiroaki Yoshida
  • Organizer: The 6th Jikji Workshop on Infinite Dimensional Analysis and Quantum Probability
  • Place of Presentation: National Iinstitute for Mathematical Sciences, Daejeon, Korea
  • Year and Date: 2010-01-10
  • Invited
• [Presentation] Remarks on the free analogue of relative entropy and of mutualinformation (2009)
  • Author(s): Hiroaki Yoshida
  • Organizer: Neumann-Zeminarium
  • Place of Presentation: Alfred Renyi Institue of Mathematics, Budapest, Hungary
  • Year and Date: 2009-11-10
  • Invited
• [Presentation] Remarks on the free analogues of relative entropy and of mutual information (2009)
  • Author(s): Hiroaki Yoshida
  • Organizer: Von Neumann Seminar
  • Place of Presentation: BME, Budapest, Hungary
  • Year and Date: 2009-11-10
• [Presentation] Linked partitions and deformed Meixner laws (2009)
  • Author(s): Hiroaki Yoshida
  • Organizer: The 12th Workshop : Non-Commutative Harmonic Analysis
  • Place of Presentation: The Mathematical Research and Conference Center Banach Institute, Bedlewo, Poland
  • Year and Date: 2009-08-20
  • Invited
• [Presentation] Linked partitions and deformed Meixner laws (2009)
  • Author(s): Hiroaki Yoshida
  • Organizer: 12th WORKSHOP : NON-COMMUTATIVE HARM ONIC ANALYSIS, Polish Academy of Sciences
  • Place of Presentation: Banach Center, Bedlewo, Poland
  • Year and Date: 2009-08-20
• [Presentation] Applications of the time derivative of the Wasserstein distance and the free entropy dissipation
  • Author(s): Hiroaki Yoshida
  • Organizer: Workshop on Analytic, Stochastic, and Operator Algebraic Aspects of Noncommutative Distributions and Free Probability
  • Place of Presentation: Fields Institute, Univ. Toronto, (Toronto, Canada)
  • Invited
• [Presentation] Applications of dissipation formulas of the relative free entropy
  • Author(s): Hiroaki Yoshida
  • Organizer: International Workshop on Noncommutative Analysis and its Future Prospects
  • Place of Presentation: Hokkaido Univ. (Sapporo, Japan)
  • Invited
• [Presentation] The free logarithmic Sobolev and transportation cost inequalities by time integration
  • Author(s): Hiroaki Yoshida
  • Organizer: The 8th Jikji Workshop on Infinite Dimensional Analysis and Quantum Probability
  • Place of Presentation: National Iinstitute for Mathematical Sciences, (Daejeon, Korea)
  • Invited
• [Presentation] 自由確率論における組合せ論的手法
  • Author(s): 吉田 裕亮
  • Organizer: CMRU 研究会「量子確率論と量子ウォーク」
  • Place of Presentation: 東北大学(Sendai, Japan)
• [Presentation] On derivation of the relative free entropy and the Talagrand's inequality for the semi-circle law
  • Author(s): Hiroaki Yoshida
  • Organizer: 15th Workshop: Non-commutative harmonic analysis
  • Place of Presentation: Banach Inst. (Bedlewo, Poland)
  • Invited
• [Presentation] The free Poisson limit by the free Fisher information distance
  • Author(s): Hiroaki Yoshida
  • Organizer: Sapporo Workshop on Non-Commutative Analysis and Applications to Complex Phenomena
  • Place of Presentation: 北海道大学（Sapporo, Japan）
• [Presentation] Integral representations of the relative free entropy associated with semicircular gradients
  • Author(s): Hiroaki Yoshida
  • Organizer: 14th Workshop: Non-commutative harmonic analysis
  • Place of Presentation: Banach Inst. (Bedlewo, Poland)
  • Invited
• [Presentation] 相対自由エントロピーの積分表示について
  • Author(s): 吉田 裕亮
  • Organizer: RIMS研究集会「独立性と従属性の数理」
  • Place of Presentation: 京都大学(Kyoto, Japan)