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

References in corpus (3)

• Polynuclear growth on a flat substrate and edge scaling of GOE eigenvalues
• Pfaffian Expressions for Random Matrix Correlation Functions
• Correlation Functions of Asymmetric Real Matrices

Cited by in corpus (2)

• Z-measures on partitions related to the infinite Gelfand pair $(S(2\infty ),H(\infty ))$
• The z-measures on partitions, Pfaffian point processes, and the matrix hypergeometric kernel