The Annals of Probability

Airy point process at the liquid-gas boundary

Vincent Beffara, Sunil Chhita, and Kurt Johansson

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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

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

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

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Mathematical Reviews number (MathSciNet)

Primary: 60G55: Point processes 82B20: Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Domino tilings Airy kernel point process two-periodic Aztec diamond


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.

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