Published April 1, 2014
| public
Journal Article
Asymptotically liberating sequences of random unitary matrices
- Creators
- Anderson, Greg W.
- Farrell, Brendan
Abstract
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.
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.Additional details
- Eprint ID
- 45922
- Resolver ID
- CaltechAUTHORS:20140527-113337111
- N00014-08-1-0883
- Office of Naval Research (ONR)
- N00014-11-1002
- Office of Naval Research (ONR)
- Alfred P. Sloan Foundation
- Created
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2014-05-27Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field