Journal of Statistical Physics. Vol. 86, Nos. 1/2, 1997. p. 109-147.
This paper is devoted to the rigorous proof of the universality conjecture of random matrix theory, according to which the limiting eigenvalue statistics of n x n random matrices within spectral intervals of O(1/n) is determined by the type of matrix (real symmetric, Hermitian, or quaternion real) and by the deqsity of states. We prove this conjecture for a certain class of the Hermitian matrix ensembles that arise in the quantum field theory and have the unitary invariant distribution defined by a certain function (the potential in the quantum field theory) satisfying some regularity conditions.