ИСТИНА

In this talk we consider ensembles of random symmetric matrices with random field type dependence. Suppose that the entries of the matrix have zero mean and finite vari- ances which can be different numbers. Assuming that the average of the normalized sums of variances in each row converges to one and Lindeberg condition holds true we prove that the empirical spectral distribution of eigenvalues converges to Wigners semicircle law. We also provide analogue of this result for sample covariance matri- ces and prove convergence of the empirical spectral distribution of eigenvalues to the Marchenko-Pastur law. This talk is based on the joint works of F. Goetze, A. Naumov and A. Tikhomirov.