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Kurt Johansson: On the rough-smooth interface in the two-periodic Aztec diamond

Time: Tue 2019-11-12 15.15 - 16.15

Location: KTH F11

Participating: Kurt Johansson, KTH

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I will discuss the structure of the boundary at the rough-smooth (or liquid-gas) interface in a random tiling model called the two-periodic Aztec diamond. This model has two types of interfaces. One between the frozen and rough phases, and one between the rough and smooth phases. At the frozen-rough interface we have a well-defined boundary path which converges to the Airy process well known from random matrix theory and random growth models. At the rough-smooth smooth boundary the situation is more complicated although here also we expect to have an Airy process. Which geometric structure converges to the Airy process? At this boundary we see both local and long range structures. The long range structures are clearly visible in simulations but to really understand them is difficult. There should be a last path among the long range structures that converges to the Airy process. We will not prove this but discuss some results in this direction. This is joint work with Vincent Beffara and Sunil Chhita.