Convergence of the spectral measure of non-normal matrices
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- by Alice Guionnet, Philip Matchett Wood and Ofer Zeitouni PDF
- Proc. Amer. Math. Soc. 142 (2014), 667-679 Request permission
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 $a$.References
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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
- Email: aguionne@ens-lyon.fr
- Philip Matchett Wood
- Affiliation: Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, Wisconsin 53706-1388
- Email: pmwood@math.wisc.edu
- 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
- MR Author ID: 186850
- ORCID: 0000-0002-2520-1525
- Email: zeitouni@math.umn.edu
- 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
- © Copyright 2013 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 142 (2014), 667-679
- MSC (2010): Primary 60B20
- DOI: https://doi.org/10.1090/S0002-9939-2013-11761-2
- MathSciNet review: 3134007