Correlation Kernels for Discrete Symplectic and Orthogonal Ensembles

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.

45 pages, added references

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Cited by in corpus (7)

• Discrete analogues of Macdonald-Mehta integrals
• Z-measures on partitions related to the infinite Gelfand pair $(S(2\infty ),H(\infty ))$
• Pfaffian Stochastic Dynamics of Strict Partitions
• The z-measures on partitions, Pfaffian point processes, and the matrix hypergeometric kernel
• Classical skew orthogonal polynomials in a two-component log-gas with charges $+1$ and $+2$
• Classical discrete symplectic ensembles on the linear and exponential lattice: skew orthogonal polynomials and correlation functions
• Pfaffian L-ensembles related to the z-measures on partitions with the Jack parameters 1/2 or 2