Airy Point Process at the liquid-gas boundary

Beffara, Vincent; Chhita, Sunil; Johansson, Kurt

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: Nov 20, 2017
• 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
• Public URL: https://durham-repository.worktribe.com/output/1343617