Cookies

We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Department of Mathematical Sciences

Staff

Publication details

Beffara, Vincent, Chhita, Sunil & Johansson, Kurt (2018). Airy Point Process at the liquid-gas boundary. Annals of Probability 46(5): 2973-3013.

Author(s) from Durham

Abstract

Domino tilings of the two-periodic Aztec diamond feature all of the three possible types
of phases of random tiling models. These phases are determined by the decay of correlations between
dominoes and are generally known as solid, liquid and gas. The liquid-solid boundary is easy to
define microscopically and is known in many models to be described by the Airy process in the limit
of a large random tiling. The liquid-gas boundary has no obvious microscopic description. Using
the height function we define a random measure in the two-periodic Aztec diamond designed to
detect the long range correlations visible at the liquid-gas boundary. We prove that this random
measure converges to the extended Airy point process. This indicates that, in a sense, the liquid-gas
boundary should also be described by the Airy process.