一个非交换的推广的de Finetti定理
A noncommutative extended de Finetti theorem
摘要：
推广的de Finetti定理刻画了可交换无限随机序列的条件独立同分布性。并证明了扩散性的分布对称性明显较弱与交换性等价。我们的主要结果是这个定理的一个非交换版本。与Ryll-Nadzewski的经典结果相反，对于无限非交换随机序列，交换性强于扩散性。从我们的调查中出现了非交换条件独立的冯诺依曼代数结构密切相关的波帕的概念交换平方和Kümmerer的广义伯努利位移。我们的主要结果适用于古典概率、量子概率，特别是自由概率、辫群表示和Jones子因子.
英文摘要：
The extended de Finetti theorem characterizes exchangeable infinite random sequences as conditionally i.i.d. and shows that the apparently weaker distributional symmetry of spreadability is equivalent to exchangeability. Our main result is a noncommutative version of this theorem. In contrast to the classical result of Ryll-Nadzewski, exchangeability turns out to be stronger than spreadability for infinite noncommutative random sequences. Out of our investigations emerges noncommutative conditional independence in terms of a von Neumann algebraic structure closely related to Popa's notion of commuting squares and Kümmerer's generalized Bernoulli shifts. Our main result is applicable to classical probability, quantum probability, in particular free probability, braid group representations and Jones subfactors.
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