An exact formula for general spectral correlation function of random Hermitian matrices

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We have found an exact formula expressing a general correlation function containing both products and ratios of characteristic polynomials of random Hermitian matrices. The answer is given in the form of a determinant. An essential difference from the previously studied correlation functions (of products only) is the appearance of non-polynomial functions along with the orthogonal polynomials. These non-polynomial functions are the Cauchy transforms of the orthogonal polynomials. The result is valid for any ensemble of beta=2 symmetry class and generalizes recent asymptotic formulae obtained for GUE and its chiral counterpart by different methods..
published version, with a few misprints corrected

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Mathematical Physics, Condensed Matter, High Energy Physics - Theory, Exactly Solvable and Integrable Systems

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http://salesiana.dossiersoluciones.com/handle/123456789/184566

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math-ph/0204051
 http://arxiv.org/abs/math-ph/0204051
 J.Phys.A36:3203-3214,2003
 doi:10.1088/0305-4470/36/12/320

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arXiv