Speaker
Prof.
Arno Kuijlaars
(Katholieke Universiteit Leuven)
Description
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 matrix valued. 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.
Reference:
M. Duits and A.B.J. Kuijlaars,
The two periodic Aztec diamond and matrix valued orthogonal polynomials,
J. Eur. Math. Soc. 23 (2021), 1075-1131.
Primary author
Prof.
Arno Kuijlaars
(Katholieke Universiteit Leuven)
Co-author
Prof.
Maurice Dutis
(KTH Stockholm)
