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

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

2008-12-19

arxiv.org/abs/0812.3817v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

32 pages, 3 figures; small corrections made

Scientific paper

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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