Asymptotically liberating sequences of random unitary matrices
Asymptotically liberating sequences of random unitary matrices
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DOI：
10.1016/j.aim.2013.12.026
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发表时间：
2014-04-01
影响因子：
1.7
通讯作者：
Farrell, Brendan
中科院分区：
文献类型：
--
作者：
Anderson, Greg W.;Farrell, Brendan
自由概率论的一个基本结果是Voiculescu提出的，后来被许多作者改进，它指出独立的Haar分布随机酉矩阵的共轭提供了渐近自由性。在本文中，我们展示了许多其他系统的随机酉矩阵，当用于共轭，导致freeness。我们这样做，首先证明一个一般结果断言“渐近解放”在相当温和的条件下，然后我们解释如何专门利用阿达玛矩阵在一个惊人的方式，这些一般结果。特别是，我们恢复和推广的第二个命名的作者和图利诺，凯尔，沙迈和Verdu的结果。(C)2014爱思唯尔公司All rights reserved.
A fundamental result of free probability theory due to Voiculescu and subsequently refined by many authors states that conjugation by independent Haar-distributed random unitary matrices delivers asymptotic freeness. In this paper we exhibit many other systems of random unitary matrices that, when used for conjugation, lead to freeness. We do so by first proving a general result asserting "asymptotic liberation" under quite mild conditions, and then we explain how to specialize these general results in a striking way by exploiting Hadamard matrices. In particular, we recover and generalize results of the second-named author and of Tulino, Caire, Shamai and Verdu. (C) 2014 Elsevier Inc. All rights reserved.