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The Two-Periodic Aztec Diamond and Matrix Valued Orthogonality

[HYBRID WORKSHOP] Integrable Structures in Random Matrix Theory and Beyond October 18, 2021 - October 22, 2021

October 20, 2021 (09:10 AM PDT - 10:00 AM PDT)
Speaker(s): Arno Kuijlaars (Katholieke Universiteit Leuven)
Location: MSRI: Simons Auditorium, Online/Virtual
Tags/Keywords
  • random tilings

  • orthogonality

  • asymptotics

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Abstract

I will discuss how polynomials with a non-hermitian orthogonality on a contour in the complex plane arise in certain random tiling problems. In the case of periodic weightings the orthogonality is matrixvalued. In work with Maurice Duits (KTH Stockholm) the Riemann-Hilbert problem for matrix valued orthogonal polynomials was used to obtain asymptotics for domino tilings of the two-periodic Aztec diamond. This model is remarkable since it gives rise to a gaseous phase, in addition to the more common solid and liquid phases.

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