ИСТИНА

One of the main questions studied in Random Matrix Theory is the asymptotic universality of the distribution of spectra of random matrices when their dimension goes to infinity. The universality means the dependence on a few global characteristics of the distribution of the matrix entries. This holds, for example, for the spectra of Hermitian random matrices with independent entries (up to symmetry), and the spectrum of non Hermitian random matrices with independent identically distributed entries. In this talk we show the asymptotic universality of the distribution of spectra of random matrices with correlated entries. In this case the limiting distribution is given by Girko’s elliptic law. We also study the product of such matrices and show that the limiting distribution for spectra doesn’t depend on correlation between matrix entries and is given by the m-th power of random variable uniformly distributed on the unit circle. The talk is based on the joint work with F. Goetze and A. Tikhomirov.