Wiener-Hopf factorizations and matrix-valued orthogonal polynomials

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.

References in corpus (7)

• Local statistics of lattice dimers
• Matrices coupled in a chain. I. Eigenvalue correlations
• Properties of Matrix Orthogonal Polynomials via their Riemann-Hilbert Characterization
• Riemann--Hilbert problems, matrix orthogonal polynomials and discrete matrix equations with singularity confinement
• Arctic curves of the octahedron equation
• A periodic hexagon tiling model and non-Hermitian orthogonal polynomials
• On the domino shuffle and matrix refactorizations