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Sbornik: Mathematics, 2011, Volume 202, Issue 2, Pages 155–206
DOI: https://doi.org/10.1070/SM2011v202n02ABEH004142 (Mi sm7702) 		 
This article is cited in 42 scientific papers (total in 43 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
English version PDF (1103 kB) Citations (43)
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DOI: https://doi.org/10.1070/SM2011v202n02ABEH004142
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.
Received: 28.01.2010 and 22.11.2010
Russian version:
Matematicheskii Sbornik, 2011, Volume 202, Number 2, Pages 3–56
DOI: https://doi.org/10.4213/sm7702
Bibliographic databases:
Document Type: Article
UDC: 517.53
MSC: 60B20, 42C05
Language: English
Original paper language: Russian
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
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  • https://www.mathnet.ru/eng/sm/v202/i2/p3
    • This publication is cited in the following 43 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:86
    First page:62
     
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