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Multiple orthogonal polynomials, string equations and the large-n limit

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Martínez Alonso, Luis and Medina Reus, Elena (2009) Multiple orthogonal polynomials, string equations and the large-n limit. Journal of physics A: Mathematical and theoretical, 42 (20). ISSN 1751-8113

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Official URL: http://dx.doi.org/10.1088/1751-8113/42/20/205204




Abstract

The Riemann-Hilbert problems for multiple orthogonal polynomials of types I and II are used to derive string equations associated with pairs of Lax-Orlov operators. A method for determining the quasiclassical limit of string equations in the phase space of the Whitham hierarchy of dispersionless integrable systems is provided. Applications to the analysis of the large-n limit of multiple orthogonal polynomials and their associated random matrix ensembles and models of non-intersecting Brownian motions are given.


Item Type:Article
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©IOP Publishing Ltd.
The authors wish to thank the Spanish Ministerio de Educación y Ciencia (research project FIS2008-00200/FIS) for its finantial support. This work is also part of the MISGAM programme of the European Science Foundation.

Uncontrolled Keywords:Gaussian random matrices; Nonintersecting brownian motions; Universal whitham hierarchy; External source; Models
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:34240
Deposited On:17 Nov 2015 19:07
Last Modified:10 Dec 2018 15:09

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