一个迹量子中心极限定理
A tracial quantum central limit theorem
摘要：
本文证明了具有迹态的von Neumann代数中非交换随机变量的中心极限定理：任何独立同分布的平均值的非交换多项式。样本收敛到经典极限。证明是基于有序联合分布的中心极限定理以及与Baker-Campbell-Hausdorff展开相关的交换子估计。这个结果可以被认为是Johansson关于固定字母表中的随机单词的形状随着其长度趋于无穷大而极限分布的定理的推广[math.CO/9906120，math. PR/9909104]。
英文摘要：
We prove a central limit theorem for non-commutative random variables in a von Neumann algebra with a tracial state: Any non-commutative polynomial of averages of i.i.d. samples converges to a classical limit. The proof is based on a central limit theorem for ordered joint distributions together with a commutator estimate related to the Baker-Campbell-Hausdorff expansion. The result can be considered a generalization of Johansson's theorem on the limiting distribution of the shape of a random word in a fixed alphabet as its length goes to infinity [math.CO/9906120,math.PR/9909104].
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