  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.
