Convergence of the spectral measure of non-normal matrices

Convergence of the spectral measure of non-normal matrices

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 t...

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Bibliographic Details
Main Authors: Guionnet, Alice (Contributor), Wood, Philip Matchett (Author), Zeitouni, Ofer (Author)
Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor)
Format: Article
Language:English
Published: American Mathematical Society (AMS), 2015-01-20T21:15:54Z.
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Summary: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.
France. Agence nationale de la recherche (Project ANR-08-BLAN-0311-01)

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