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

Yan V. Fyodorov*, Eugene Strahov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

79 Scopus citations

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

Original languageAmerican English
Pages (from-to)3203-3213
Number of pages11
JournalJournal of Physics A: Mathematical and General
Volume36
Issue number12 SPEC. ISS.
DOIs
StatePublished - 28 Mar 2003
Externally publishedYes

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