Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
Volume 36, Issue 12, Pages 3203-3213Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0305-4470/36/12/320
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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 arbitrary ensemble of beta = 2 symmetry class and generalizes recent asymptotic formulae obtained for Gaussian unitary ensemble and its chiral counterpart by different methods.
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