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arXiv · 2402.07706

Wiener-Hopf factorizations and matrix-valued orthogonal polynomials

Arno B. J. Kuijlaars·Mateusz Piorkowski
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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 $2 \times 2$-periodic Aztec diamond in terms of Jacobi theta functions related to the spectral curve of the model.

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Arno B. J. Kuijlaars, Mateusz Piorkowski. 2024-02-12. Wiener-Hopf factorizations and matrix-valued orthogonal polynomials. https://doi.org/10.2140/pmp.2025.6.547

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