Convergence of the spectral measure of non-normal matrices
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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.
Date issued
2013-10Department
Massachusetts Institute of Technology. Department of MathematicsJournal
Proceedings of the American Mathematical Society
Publisher
American Mathematical Society (AMS)
Citation
Guionnet, Alice, Philip Matchett Wood, and Ofer Zeitouni. "Convergence of the spectral measure of non-normal matrices." Proc. Amer. Math. Soc. 142 (2014), 667-679. © 2013 American Mathematical Society
Version: Final published version
ISSN
0002-9939
1088-6826