Convergence of the spectral measure of non normal matrices

Details Convergence of the spectral measure of non normal matrices Convergence of the spectral measure of non normal matrices

2011-10-11

arxiv.org/abs/1110.2471v1

Mathematics

Probability

Scientific paper

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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