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

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dc.creatorFyodorov, Yan V.
dc.creatorStrahov, Eugene
dc.date2002-04-26
dc.date2003-05-09
dc.date.accessioned2026-07-07T10:50:32Z
dc.date.available2026-07-07T10:50:32Z
dc.descriptionWe 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..
dc.descriptionpublished version, with a few misprints corrected
dc.identifierhttps://arxiv.org/abs/math-ph/0204051
dc.identifierhttp://arxiv.org/abs/math-ph/0204051
dc.identifierJ.Phys.A36:3203-3214,2003
dc.identifierdoi:10.1088/0305-4470/36/12/320
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/184566
dc.subjectMathematical Physics
dc.subjectCondensed Matter
dc.subjectHigh Energy Physics - Theory
dc.subjectExactly Solvable and Integrable Systems
dc.titleAn exact formula for general spectral correlation function of random Hermitian matrices
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