Convergence of the spectral measure of non-normal matrices. (English) Zbl 1302.60020
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 \(\ast\)-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 \(a\).
MSC:
| 60B20 | Random matrices (probabilistic aspects) |
Keywords:
regularization by noise; spectrum of large random non-normal matrices; Gaussian Ginibre matrixSoftware:
EigtoolReferences:
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