ИСТИНА

We consider ensemble of real random matrices with correlated entries. This ensemble extends the ensemble of random matrices with independent entries and the ensemble of symmetric random matrices. Assume that the matrix entries are non identically distributed and have uniformly integrable second moment. It is well known that the empirical spectral measure of the eigenvalues weakly converges in probability to the uniform distribution on the ellipse. The axes of the ellipse are determined by the correlation between matrix entries. This result is called "Girko’s elliptic law". In this talk we consider the product of m>=2 such random matrices and prove that the empirical spectral measure of the eigenvalues weakly converges in probability to the distribution of m-th power of the random variable uniformly distributed on the unit disc. The limit distribution doesn’t depend on correlation between matrix entries. The talk is based on the joint work with F. Goetze and A. Tikhomirov.