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

VIENNA PROBABILITY SEMINAR

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. Previously, 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 talk, we discuss the local geometric picture give a conjecture for the local geometry at the rough-smooth interface. This is joint work with Kurt Johansson and Vincent Beffara.