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 $Z_2$ symmetric distribution 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.

15 pages, LaTex, a paragraph added in note added:, three references added. accepted in Nucl. Phys.B

References in corpus (2)

• Renormalization group approach to multiple-arc random matrix models
• Universal correlations in random matrices: quantum chaos, the $1/r^2$ integrable model, and quantum gravity

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