Orthogonal polynomials and exact correlation functions for two cut random matrix models

Abstract

Exact eigenvalue correlation functions are computed for large N hermitian one-matrix models with eigenvalues distributed in two symmetric cuts. An asymptotic form for orthogonal polynomials for arbitrary polynomial potentials that support a Z 2 symmetricdistribution is obtained. This results in an exact explicit expression for the kernel at large N which determines all eigenvalue correlators. The oscillating and smooth parts of the two-point correlator are extracted and the universality of local fine-grained and smoothed global correlators is established.