Title: Multiple Meixner-Pollaczek polynomials and the six-vertex model
Authors: Bender, Martin ×
Delvaux, Steven
Kuijlaars, Arno #
Issue Date: Nov-2011
Publisher: Academic Press
Series Title: Journal of Approximation Theory vol:163 issue:11 pages:1606-1637
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.
ISSN: 0021-9045
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

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