Asymptotically liberating sequences of random unitary matrices

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• 作者：Greg W. Anderson^a ; ^{gwanders@umn.edu" class="auth_mail} ; Brendan Farrell^b ; ¹ ; ^{farrell@cms.caltech.edu" class="auth_mail}
• 关键词：60B20 ; 42A61 ; 46L54 ; 15B52
• 刊名：Advances in Mathematics
• 出版年：1 April, 2014
• 年：2014
• 卷：255
• 期：Complete
• 页码：381-413
• 全文大小：446 K

文摘

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 鈥渁symptotic liberation鈥?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 Verd煤.