For a symmetric subclass of 3x3-periodic hexagon tilings, the associated matrix valued orthogonal polynomials admit a full asymptotic expansion built from an explicit balayage equilibrium measure on a genus one spectral curve.
Bain, Local correlation functions of the two-periodic weighted Aztec diamond in mesoscopic limit, J
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Matrix valued orthogonal polynomials arising from hexagon tilings with 3x3-periodic weightings
For a symmetric subclass of 3x3-periodic hexagon tilings, the associated matrix valued orthogonal polynomials admit a full asymptotic expansion built from an explicit balayage equilibrium measure on a genus one spectral curve.