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

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

2002-04-26

arxiv.org/abs/math-ph/0204051v4

J.Phys.A36:3203-3214,2003

Physics

Mathematical Physics

published version, with a few misprints corrected

Scientific paper

10.1088/0305-4470/36/12/320

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..

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