Local geometry of the rough-smooth interface in the two-periodic Aztec diamond.

Random tilings of the two-periodic Aztec diamond contain three
macroscopic regions: frozen, where the tilings are deterministic; rough,
where the correlations between dominoes decay polynomially; smooth,
where the correlations between dominoes decay exponentially. In a
previous paper, we found that a certain averaging of the height function
at the rough smooth interface converged to the extended Airy kernel
point process. In this paper, we augment the local geometrical picture
at this interface by introducing well-defined lattice paths which are
closely related to the level lines of the height function. We show after
suitable centering and rescaling that a point process from these paths
converge to the extended Airy kernel point process provided that the
natural parameter associated to the two-periodic Aztec
diamond is small enough. This is joint work with Kurt Johansson and
Vincent Beffara.

• Speaker: Sunil Chhita (Durham)
• Tuesday 11 February 2020, 14:00–15:00
• Venue: MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.
• Series: Probability; organiser: Perla Sousi.