Deformations of independence on non-commutative probability spaces and deformed Fock spaces

2008 Fiscal Year Final Research Report

• Project/Area Number: 17540190
• 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 Ochanomizu University, 大学院・人間文化創成科学研究科, 教授 (10220667)
• Co-Investigator(Kenkyū-buntansha): YANO Yuko お茶の水女子大学, 理学部, アソシエートフエロー (10337462)
• Project Period (FY): 2005 – 2008
• Keywords: 非可換確率論 / 作用素環論 / 変形量子化 / 量子確率論 / 変形合成積

Research Abstract

本研究では, 非可換(量子)確率空間における独立性の変形をモーメント・キュムラント関係式の変形と捉えることにより, 順序集合の分割統計の理論と確率分布の変形理論との関係, さらに構成された変形独立性を実現する非可換確率空間のモデルをフォック空間の変形で与える研究を行った.

Research Products

• [Journal Article] Remarks on a semicircular perturbation of the free Fisher in formation, Infin. Dimens (2008)
  • Author(s): Hiroaki Yoshida
  • Journal Title: Anal. Quantum Probab. Relat. Top. 11 Pages: 97-108
  • Peer Reviewed
• [Journal Article] Some set partition statistics in non-crossing partitions and generating functions (2007)
  • Author(s): Fujine Yano, Hiroaki Yoshida
  • Journal Title: Discrete Mathematics 307 Pages: 127-140
  • Peer Reviewed
• [Journal Article] Generalized q-deformed Gaussian random variables (2006)
  • Author(s): Marek Bozejko, Hiroaki Yoshida
  • Journal Title: Publication Banach Institute 73 Pages: 127-140
  • Peer Reviewed
• [Presentation] Meixner operators on the q-Fock space and Schrodinger Algebra (2008)
  • Author(s): Hiroaki Yoshida
  • Organizer: The 8th Sendai Workshop on Infinite Dimensional Analysis and Quantum Probability
  • Year and Date: 20081100
• [Presentation] Remarks on non-crossing "linked" partitions and free Meixner law (2008)
  • Author(s): Hiroaki Yoshida
  • Organizer: 1th WORKSHOP : NON-COMMUTATI VE HARMONIC ANALYSIS WITH APPLICATIONS TO PROBABILITY
  • Place of Presentation: Banach Center, Poland(招待講演)
  • Year and Date: 20080800
• [Presentation] Alternative proofs of the free Fisher information and the free entropy power inequalities (2008)
  • Author(s): Hiroaki Yoshida
  • Organizer: 10th WORKSHOP : NON-COMMUTATI VE HARMONIC ANALYSIS WITH APPLICATIONS TO PROBABILITY
  • Place of Presentation: Banach Center, Poland(招待講演)
  • Year and Date: 20080800
• [Presentation] 非可換確率空間における独立性の変形 (2005)
  • Author(s): 吉田裕亮
  • Organizer: 日本数学会2005年度秋季総合分科会
  • Place of Presentation: 岡山(特別講演)
  • Year and Date: 20050900