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arXiv · 1110.2471

Convergence of the spectral measure of non normal matrices

Alice Guionnet·Philip Matchett Wood·Ofer Zeitouni
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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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Alice Guionnet, Philip Matchett Wood, Ofer Zeitouni. 2011-10-11. Convergence of the spectral measure of non normal matrices. https://arxiv.org/abs/1110.2471

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