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自由Fisher信息量与合并自由

孟彬 郭懋正 曹小红

孟彬, 郭懋正, 曹小红. 自由Fisher信息量与合并自由[J]. 应用数学和力学, 2004, 25(10): 1007-1013.
引用本文: 孟彬, 郭懋正, 曹小红. 自由Fisher信息量与合并自由[J]. 应用数学和力学, 2004, 25(10): 1007-1013.
MENG Bin, GUO Mao-zheng, CAO Xiao-hong. Free Fisher Information and Amalgamated Freeness[J]. Applied Mathematics and Mechanics, 2004, 25(10): 1007-1013.
Citation: MENG Bin, GUO Mao-zheng, CAO Xiao-hong. Free Fisher Information and Amalgamated Freeness[J]. Applied Mathematics and Mechanics, 2004, 25(10): 1007-1013.

自由Fisher信息量与合并自由

详细信息
    作者简介:

    孟彬(1976- ),男,山东泰安人,博士(E-mail:b.meng@pku.edu.cn);郭懋正,男,教授,博士生导师(联系人.Tel:+86-10-62752163;E-mail:maguo@pku.edu.cn)

  • 中图分类号: O177.1

Free Fisher Information and Amalgamated Freeness

  • 摘要: 在算子值非交换概率空间中引入算子值自由Fisher信息量的概念,这一定义是对D.Voiculescu在有迹的von Neumann代数上定义的自由Fisher信息量的推广.证明了算子值自由Fisher信息量与合并自由性是密切相关的,即证明了若干个算子值随机变量的自由Fisher信息量的可加性等价于这些随机变量的合并自由性.并且也类似地得到了Cramer-Rao不等式.
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    [2] Ge L.Applications of free entropy to finite von Neumann algebras Ⅱ[J].Annals of Mathematics,1998,147(2):143—157. doi: 10.2307/120985
    [3] Voiculescu D.The analogues of entropy and of Fisher's information measure in free probability theory—Ⅴ:Noncommutative Hilbert transforms[J].Inventiones Mathematicae,1998,132(1):189—227. doi: 10.1007/s002220050222
    [4] Voiculescu D.The analogues of entropy and of Fisher's information measure in free probability theory—Ⅵ:liberation and mutual free information[J].Advances in Mathematics,1999,146(1):101—166. doi: 10.1006/aima.1998.1819
    [5] Voiculescu D.Operations on certain non-commutative operator-valued random variables[J].Astérisque,1995,232(1):243—275.
    [6] Sunder V S.An Invitation to von Neumann Algebras[M].New York:Springer-Verlag,1987.
    [7] Cover T M,Thomas J A.Elements of Information Theory[M].Chichester:John Wiley & Sons,Inc,1976.
    [8] Speicher R.Combinatorial theory of the free product with amalgamation and operator-valued free probability theory[J].Memoirs of AMS,1998,(627):1—88.
    [9] Nica A,Shlyakhtenko D,Speicher R.Operator-valued distributions—1:characterizations of freeness[J].International Mathematics Research Notices,2002,(29):1509—1538.
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出版历程
  • 收稿日期:  2003-06-15
  • 修回日期:  2004-06-15
  • 刊出日期:  2004-10-15

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