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Convergence of the spectral measure of non-normal matrices

Authors: Alice Guionnet, Philip Matchett Wood and Ofer Zeitouni
Journal: Proc. Amer. Math. Soc. 142 (2014), 667-679
MSC (2010): Primary 60B20
Published electronically: October 8, 2013
MathSciNet review: 3134007
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Abstract: We discuss regularization by noise of the spectrum of large random non-normal matrices. Under suitable conditions, we show that the regularization of a sequence of matrices that converges in $ *$-moments to a regular element $ a$ by the addition of a polynomially vanishing Gaussian Ginibre matrix forces the empirical measure of eigenvalues to converge to the Brown measure of $ a$.

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Additional Information

Alice Guionnet
Affiliation: UMPA, CNRS UMR 5669, ENS Lyon, 46 allée d’Italie, 69007 Lyon, France
Address at time of publication: Department of Mathematics, Room 2-272, Massachusetts Institute of Technology, Cambridge, Massachusetts 02134

Philip Matchett Wood
Affiliation: Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, Wisconsin 53706-1388

Ofer Zeitouni
Affiliation: School of Mathematics, University of Minnesota, 206 Church Street SE, Minneapolis, Minnesota 55455—and—Faculty of Mathematics, Weizmann Institute, POB 26, Rehovot 76100, Israel
Address at time of publication: Faculty of Mathematics, Weizmann Institute, POB 26, Rehovot 76100, Israel

Received by editor(s): October 11, 2011
Received by editor(s) in revised form: October 22, 2011, March 4, 2012, and March 15, 2012
Published electronically: October 8, 2013
Additional Notes: The work of the first author was partially supported by ANR project ANR-08-BLAN-0311-01
The work of the third author was partially supported by NSF grant DMS-0804133 and by a grant from the Israel Science Foundation
Communicated by: Marius Junge
Article copyright: © Copyright 2013 American Mathematical Society

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