Multiple orthogonal polynomials, string equations and the large-n limit
Exactly Solvable and Integrable Systems
2009-01-05 v2 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.0812.3817,
title = {Multiple orthogonal polynomials, string equations and the large-n limit},
author = {L. Martinez Alonso and E. Medina},
journal= {arXiv preprint arXiv:0812.3817},
year = {2009}
}
Comments
32 pages, 3 figures; small corrections made