关于Haar酉矩阵的部分转置

IF 0.7 3区数学 Q2 MATHEMATICS

Studia Mathematica Pub Date : 2021-05-10 DOI:10.4064/sm210517-13-12

J. Mingo, M. Popa, K. Szpojankowski

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引用次数: 3

摘要

研究了一个Haar分布随机酉矩阵的偏转置对其极限*分布的影响。如果我们确定块的数目b，我们证明了偏转置可以沿着对角线分解成b个矩阵的和，这些矩阵是渐近自由且同分布的。然后，我们考虑了不同块分解的联合效应，并证明在一些温和的假设下，我们也得到了渐近自由。

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On the partial transpose of a Haar unitary matrix

We consider the effect of a partial transpose on the limit ∗-distribution of a Haar distributed random unitary matrix. If we fix the number of blocks, b, we show that the partial transpose can be decomposed along diagonals into a sum of b matrices which are asymptotically free and identically distributed. We then consider the joint effect of different block decompositions and show that under some mild assumptions we also get asymptotic freeness.

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来源期刊

Studia Mathematica 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

5 months

期刊介绍： The journal publishes original papers in English, French, German and Russian, mainly in functional analysis, abstract methods of mathematical analysis and probability theory.