English

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

R2 v1 2026-06-21T11:54:09.784Z