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• W3104449911 abstract "It has been shown recently [10] that Cauchy transforms of orthogonal polynomials appear naturally in general correlation functions containing ratios of characteristic polynomials of random NxN Hermitian matrices. Our main goal is to investigate the issue of universality of large N asymptotics for those Cauchy transforms for a wide class of weight functions. Our analysis covers three different scaling regimes: the hard edge, the bulk and the soft edge of the spectrum, thus extending the earlier results known for the bulk. The principal tool is to show that for finite matrix size N the auxiliary wave functions associated with the Cauchy transforms obey the same second order differential equation as those associated with the orthogonal polynomials themselves." @default.
• W3104449911 created "2020-11-23" @default.
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• W3104449911 date "2003-08-01" @default.
• W3104449911 modified "2023-09-25" @default.
• W3104449911 title "Universal random matrix correlations of ratios of characteristic polynomials at the spectral edges" @default.
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• W3104449911 doi "https://doi.org/10.1016/s0550-3213(03)00458-9" @default.
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