Multiple Meixner-Pollaczek polynomials and the six-vertex model
Abstract
We study multiple orthogonal polynomials of Meixner-Pollaczek type with respect to a symmetric system of two orthogonality measures. Our main result is that the limiting distribution of the zeros of these polynomials is one component of the solution to a constrained vector equilibrium problem. We also provide a Rodrigues formula and closed expressions for the recurrence coefficients. The proof of the main result follows from a connection with the eigenvalues of block Toeplitz matrices, for which we provide some general results of independent interest. The motivation for this paper is the study of a model in statistical mechanics, the so-called six-vertex model with domain wall boundary conditions, in a particular regime known as the free fermion line. We show how the multiple Meixner-Pollaczek polynomials arise in an inhomogeneous version of this model.
Cite
@article{arxiv.1101.2982,
title = {Multiple Meixner-Pollaczek polynomials and the six-vertex model},
author = {Martin Bender and Steven Delvaux and Arno B. J. Kuijlaars},
journal= {arXiv preprint arXiv:1101.2982},
year = {2011}
}
Comments
32 pages, 4 figures. References added