Concentration and convergence rates for spectral measures of random matrices

Details Concentration and convergence rates for spectral measures of random matrices Concentration and convergence rates for spectral measures of random matrices

2011-09-27

arxiv.org/abs/1109.5997v2

Mathematics

Probability

16 pages, no figures. Minor revisions in response to referee comments. To appear in Probab. Theory Related Fields

Scientific paper

The topic of this paper is the typical behavior of the spectral measures of large random matrices drawn from several ensembles of interest, including in particular matrices drawn from Haar measure on the classical Lie groups, random compressions of random Hermitian matrices, and the so-called random sum of two independent random matrices. In each case, we estimate the expected Wasserstein distance from the empirical spectral measure to a deterministic reference measure, and prove a concentration result for that distance. As a consequence we obtain almost sure convergence of the empirical spectral measures in all cases.

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