Orthogonal and Symplectic Matrix Models: Universality and Other Properties

We study orthogonal and symplectic matrix models with polynomial potentials and multi interval supports of the equilibrium measures. For these models we find the bounds (similar to those for the hermitian matrix models) for the rate of convergence of linear eigenvalue statistics and for the variance of linear eigenvalue statistics and find the logarithms of partition functions up to the order O(1). We prove also the universality of local eigenvalue statistics in the bulk.