Ratios of characteristic polynomials in complex matrix models
نویسندگان
چکیده
منابع مشابه
Ratios of characteristic polynomials in complex matrix models
We compute correlation functions of inverse powers and ratios of characteristic polynomials for random matrix models with complex eigenvalues. Compact expressions are given in terms of orthogonal polynomials in the complex plane as well as their Cauchy transforms, generalizing previous expressions for real eigenvalues. We restrict ourselves to ratios of characteristic polynomials over their com...
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We calculate the expectation value of an arbitrary product of characteristic polynomials of complex random matrices and their hermitian conjugates. Using the technique of orthogonal polynomials in the complex plane our result can be written in terms of a determinant containing these polynomials and their kernel. It generalizes the known expression for hermitian matrices and it also provides a g...
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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 N × N 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...
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denotes the average of f with respect to dPa ,N . Recently there has been considerable interest in the averages of products and ratios of the characteristic polynomials DN@m ,H#5P i51 N (m2xi(H)) of random matrices with respect to various ensembles. Such averages are used, in particular, in making predictions about the moments of the Riemann-zeta function @see Refs. 12–14 ~circular ensembles! a...
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We consider asymptotics of ratios of random characteristic polynomials associated with orthogonal polynomial ensembles. Under some natural conditions on the measure in the definition of the orthogonal polynomial ensemble we establish a universality limit for these ratios. c ⃝ 2012 Elsevier Inc. All rights reserved.
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2004
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/37/37/l01