Convergence of the spectral measure of non-normal matrices
Open Access
- 8 October 2013
- journal article
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 142 (2) , 667-679
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 by the addition of a polynomially vanishing Gaussian Ginibre matrix forces the empirical measure of eigenvalues to converge to the Brown measure of .Keywords
All Related Versions
This publication has 6 references indexed in Scilit:
- The single ring theoremAnnals of Mathematics, 2011
- An Introduction to Random Matrices2009
- Smoothed Analysis of the Condition Numbers and Growth Factors of MatricesSIAM Journal on Matrix Analysis and Applications, 2006
- Random Regularization of Brown Spectral MeasureJournal of Functional Analysis, 2002
- Brown's Spectral Distribution Measure for R-Diagonal Elements in Finite von Neumann AlgebrasJournal of Functional Analysis, 2000
- Limit laws for Random matrices and free productsInventiones Mathematicae, 1991