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September 2018 Airy point process at the liquid-gas boundary
Vincent Beffara, Sunil Chhita, Kurt Johansson
Ann. Probab. 46(5): 2973-3013 (September 2018). DOI: 10.1214/17-AOP1244

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.

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Vincent Beffara. Sunil Chhita. Kurt Johansson. "Airy point process at the liquid-gas boundary." Ann. Probab. 46 (5) 2973 - 3013, September 2018. https://doi.org/10.1214/17-AOP1244

Information

Received: 1 February 2017; Revised: 1 November 2017; Published: September 2018
First available in Project Euclid: 24 August 2018

zbMATH: 06964353
MathSciNet: MR3846843
Digital Object Identifier: 10.1214/17-AOP1244

Subjects:
Primary: 60G55 , 60K35 , 82B20

Keywords: Airy kernel point process , Domino tilings , two-periodic Aztec diamond

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.46 • No. 5 • September 2018
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