Skip to Main content Skip to Navigation
Journal articles

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.
Complete list of metadata

Cited literature [36 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01632943
Contributor : Vincent Beffara Connect in order to contact the contributor
Submitted on : Wednesday, September 19, 2018 - 9:21:12 PM
Last modification on : Tuesday, May 11, 2021 - 11:36:05 AM

File

AOP1244.pdf
Publisher files allowed on an open archive

Identifiers

Collections

Citation

Vincent Beffara, Sunil Chhita, Kurt Johansson. Airy point process at the liquid-gas boundary. Annals of Probability, Institute of Mathematical Statistics, 2018, 46 (5), pp.2973 - 3013. ⟨10.1214/17-aop1244⟩. ⟨hal-01632943v2⟩

Share

Metrics

Les métriques sont temporairement indisponibles