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Mat. Sb., 2011, Volume 202, Number 2, Pages 3–56 (Mi msb7702)  

This article is cited in 30 scientific papers (total in 31 papers)

Random matrices with external source and the asymptotic behaviour of multiple orthogonal polynomials

A. I. Aptekarev, V. G. Lysov, D. N. Tulyakov

M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences

Abstract: Ensembles of random Hermitian matrices with a distribution measure defined by an anharmonic potential perturbed by an external source are considered. The limiting characteristics of the eigenvalue distribution of the matrices in these ensembles are related to the asymptotic behaviour of a certain system of multiple orthogonal polynomials. Strong asymptotic formulae are derived for this system. As a consequence, for matrices in this ensemble the limit mean eigenvalue density is found, and a variational principle is proposed to characterize this density.
Bibliography: 35 titles.

Keywords: random matrices, multiple orthogonal polynomials, strong asymptotics, matrix Riemann-Hilbert problem, extremal problems in the theory of logarithmic potentials.


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English version:
Sbornik: Mathematics, 2011, 202:2, 155–206

Bibliographic databases:

Document Type: Article
UDC: 517.53
MSC: 60B20, 42C05
Received: 28.01.2010 and 22.11.2010

Citation: A. I. Aptekarev, V. G. Lysov, D. N. Tulyakov, “Random matrices with external source and the asymptotic behaviour of multiple orthogonal polynomials”, Mat. Sb., 202:2 (2011), 3–56; Sb. Math., 202:2 (2011), 155–206

Citation in format AMSBIB
\by A.~I.~Aptekarev, V.~G.~Lysov, D.~N.~Tulyakov
\paper Random matrices with external source and the asymptotic behaviour of multiple orthogonal polynomials
\jour Mat. Sb.
\yr 2011
\vol 202
\issue 2
\pages 3--56
\jour Sb. Math.
\yr 2011
\vol 202
\issue 2
\pages 155--206

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