Speaker: Filippo Colomo
Title: Frozen boundaries and their fluctuations in the six-vertex model

Abstract:
The six-vertex model is a paradigmatic, exactly solvable model of
statistical mechanics. In the case of domain wall boundary conditions,
the model exhibits limit shape phenomena with the emergence, in the
scaling limit, of regions of order and disorder, sharply separated by
a smooth curve, called arctic curve.  The physical behaviour of the
model depends in an essential way on the anisotropy parameter
$\Delta$. When $\Delta=0$ (free-fermion point) the model is
determinantal, and corresponds to the domino tilings of an Aztec
diamond. As such, it has been studied in full detail and rigour; in
particular, the arctic curve is exactly a circle, and fluctuations
around it are governed by the Airy process and the GUE Tracy-Widom
distribution. Here we tackle such questions when $\Delta\not
0$. Specifically, we determine the exact expression of the arctic
curve for generic values of $\Delta$, and show that fluctuations
around it are again governed by the GUE Tracy-Widom distribution.

Joint work with Andrei Pronko.