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Airy Point Process at the liquid-gas boundary

Beffara, Vincent; Chhita, Sunil; Johansson, Kurt

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Authors

Vincent Beffara

Kurt Johansson



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.

Citation

Beffara, V., Chhita, S., & Johansson, K. (2018). Airy Point Process at the liquid-gas boundary. Annals of Probability, 46(5), 2973-3013. https://doi.org/10.1214/17-aop1244

Journal Article Type Article
Acceptance Date Nov 10, 2017
Online Publication Date Aug 24, 2018
Publication Date Sep 30, 2018
Deposit Date Nov 17, 2017
Publicly Available Date Mar 29, 2024
Journal Annals of Probability
Print ISSN 0091-1798
Publisher Institute of Mathematical Statistics
Peer Reviewed Peer Reviewed
Volume 46
Issue 5
Pages 2973-3013
DOI https://doi.org/10.1214/17-aop1244

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