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

Authors: Fyodorov Y.V.¹; Strahov E.

Source: Journal of Physics A: Mathematical and General, Volume 36, Number 12, 2003 , pp. 3203-3213(11)

Publisher: Institute of Physics Publishing

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Abstract:

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 2 symmetry class and generalizes recent asymptotic formulae obtained for Gaussian unitary ensemble and its chiral counterpart by different methods.

Language: English

Document Type: Miscellaneous

Affiliations: 1: On leave from Petersburg Nuclear Physics Institute, Gatchina 188350, Russia.

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