UNIVERSALITY OF THE LOCAL EIGENVALUE STATISTICS FOR A CLASS OF UNITARY INVARIANT RANDOM-MATRIX ENSEMBLES

This paper is devoted to the rigorous proof of the universality conjec ture of random matrix theory, according to which the limiting eigenval ue statistics of n x n random matrices within spectral intervals of O( n(-1)) is determined by the type of matrix (real symmetric, Hermitian, or quaternion real) and by the density of states. We prove this conje cture for a certain class of the Hermitian matrix ensembles that arise in the quantum field theory and have the unitary invariant distributi on defined by a certain function (the potential in the quantum field t heory) satisfying some regularity conditions.