Correlation Kernels for Discrete Symplectic and Orthogonal Ensembles

Alexei Borodin, Eugene Strahov

Published 2007-12-11, updated 2008-01-13Version 2

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.