Wiener-Hopf factorizations and matrix-valued orthogonal polynomials
Classical Analysis and ODEs
2025-03-12 v1 Mathematical Physics
math.MP
Probability
Abstract
We compare two methods for analysing periodic dimer models. These are the matrix-valued orthogonal polynomials approach due to Duits and one of the authors, and the Wiener-Hopf approach due to Berggren and Duits. We establish their equivalence in the special case of the Aztec diamond. Additionally, we provide explicit formulas for the matrix-valued orthogonal polynomials/Wiener-Hopf factors in the case of the -periodic Aztec diamond in terms of Jacobi theta functions related to the spectral curve of the model.
Cite
@article{arxiv.2402.07706,
title = {Wiener-Hopf factorizations and matrix-valued orthogonal polynomials},
author = {Arno B. J. Kuijlaars and Mateusz Piorkowski},
journal= {arXiv preprint arXiv:2402.07706},
year = {2025}
}