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arXiv · 0812.3817

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

L. Martinez Alonso·E. Medina
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Abstract

The Riemann-Hilbert problems for multiple orthogonal polynomials of types I and II are used to derive string equations associated to 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.

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L. Martinez Alonso, E. Medina. 2008-12-30. Multiple orthogonal polynomials, string equations and the large-n limit. https://arxiv.org/abs/0812.3817

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