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Edge Statistics for Lozenge Tilings of Polygons

Jiaoyang Huang
Monday, November 8, 2021 - 2:30pm to 3:30pm
Zoom Meeting ID: 992 8713 1654

A central feature of random lozenge tilings is that they exhibit boundary induced phase transitions. Depending on the shape of the domain, they can admit frozen regions and liquid regions. The curve separating these two phases is called the arctic boundary. For random lozenge tilings of polygonal domains, it is predicted that the arctic boundary after proper rescaling converges to the Airy process, a universal scaling limit that is believed to govern various phenomena related to the Kardar–Parisi–Zhang universality class. In this talk, I will give an overview of this edge universality phenomenon, and explain a proof for random lozenge tilings of simply connected polygons forbidding specific (presumably non-generic) behaviors for singular points of the limiting arctic boundary. This is a joint work with Amol Aggarwal.

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