## The Annals of Probability

### Airy point process at the liquid-gas boundary

#### 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.

#### Article information

Source
Ann. Probab., Volume 46, Number 5 (2018), 2973-3013.

Dates
Revised: November 2017
First available in Project Euclid: 24 August 2018

https://projecteuclid.org/euclid.aop/1535097644

Digital Object Identifier
doi:10.1214/17-AOP1244

Mathematical Reviews number (MathSciNet)
MR3846843

#### Citation

Beffara, Vincent; Chhita, Sunil; Johansson, Kurt. Airy point process at the liquid-gas boundary. Ann. Probab. 46 (2018), no. 5, 2973--3013. doi:10.1214/17-AOP1244. https://projecteuclid.org/euclid.aop/1535097644

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