Correlation Kernels for Discrete Symplectic and Orthogonal Ensembles

Details Correlation Kernels for Discrete Symplectic and Orthogonal Ensembles Correlation Kernels for Discrete Symplectic and Orthogonal Ensembles

2007-12-11

arxiv.org/abs/0712.1693v2

Physics

Mathematical Physics

45 pages, added references

Scientific paper

10.1007/s00220-008-0629-8

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.

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