EIGENVALUE DISTRIBUTION OF RANDOM MATRICES - SOME RECENT RESULTS

We review recent results obtained for the eigenvalue statistics of n x n Hermitian (real symmetric) random matrices with nonunitary (nonorth ogonal) invariant probability distributions. Most of the paper is devo ted to the normalized counting measure of eigenvalues (NCM). We descri be formulae for the nonrandom limit form (known as the integrated dens ity of states (IDS)) of this random measure corresponding to a variety of the random matrix ensembles and obtained by an unique method, base d on the study of the Stieltjes transform of the NCM. We mention also results on the 1/n corrections to the IDS and to more complex statisti cal characteristics of the eigenvalue distribution obtained by the sam e method.