Beffara, Vincent and Chhita, Sunil and Johansson, Kurt (2018) 'Airy point process at the liquid-gas boundary.', Annals of probability., 46 (5). pp. 2973-3013.
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.
|Full text:||(AM) Accepted Manuscript|
Download PDF (1844Kb)
|Full text:||(VoR) Version of Record|
Download PDF (1169Kb)
|Publisher Web site:||https://doi.org/10.1214/17-AOP1244|
|Date accepted:||10 November 2017|
|Date deposited:||20 November 2017|
|Date of first online publication:||24 August 2018|
|Date first made open access:||06 September 2018|
Save or Share this output
|Look up in GoogleScholar|