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Asymptotically liberating sequences of random unitary matrices

Anderson, Greg W. and Farrell, Brendan (2014) Asymptotically liberating sequences of random unitary matrices. Advances in Mathematics, 255 . pp. 381-413. ISSN 0001-8708. doi:10.1016/j.aim.2013.12.026.

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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 Verdú.

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Additional Information:© 2014 Elsevier Inc. Received 22 February 2013. Accepted 21 December 2013. Available online 29 January 2014. Communicated by Dan Voiculescu. B. F. is partially supported by Joel A. Tropp under ONR awards N00014-08-1-0883 and N00014-11-1002 and a Sloan Research Fellowship.
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-08-1-0883
Office of Naval Research (ONR)N00014-11-1002
Alfred P. Sloan FoundationUNSPECIFIED
Subject Keywords:Free probability; Asymptotic liberation; Random matrices; Unitary matrices; Hadamard matrices
Classification Code:MSC: 60B20; 42A61; 46L54; 15B52
Record Number:CaltechAUTHORS:20140527-113337111
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Official Citation:Greg W. Anderson, Brendan Farrell, Asymptotically liberating sequences of random unitary matrices, Advances in Mathematics, Volume 255, 1 April 2014, Pages 381-413, ISSN 0001-8708, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:45922
Deposited By: Ruth Sustaita
Deposited On:27 May 2014 19:02
Last Modified:10 Nov 2021 17:18

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