Correlation Kernels for Discrete Symplectic and Orthogonal Ensembles

TL;DR

This paper extends Widom's formulae to discrete orthogonal and symplectic ensembles, explicitly computing correlation kernels for classical Meixner and Charlier polynomials, advancing understanding of discrete random matrix models.

Contribution

It derives new correlation kernel formulas for discrete ensembles with rational discrete logarithmic derivatives, specifically for Meixner and Charlier polynomials.

Findings

Explicit correlation kernels for Meixner and Charlier ensembles.

Extension of Widom's formulae to discrete ensembles.

Enhanced analytical tools for discrete random matrix models.

Abstract

H. Widom derived formulae expressing correlation functions of orthogonal and symplectic ensembles of random matrices in terms of orthogonal polynomials (H. Widom. J. Stat. Phys. 94, (1999) 347-363). We obtain similar results for discrete ensembles whose weights have rational discrete logarithmic derivatives, and compute explicitly correlation kernels associated to the classical Meixner and Charlier orthogonal polynomials.