AIRY POINT PROCESS AT THE LIQUID-GAS BOUNDARY

• 成果类型: Article
• 署名作者: Beffara, Vincent; Chhita, Sunil; Johansson, Kurt
• 署名单位: Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Durham University; Royal Institute of Technology
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/17-AOP1244
• 发表日期: 2018
• 页码: 2973-3013
• 关键词: random lozenge tilings; gaussian free-field; aztec diamonds; domino tilings; schur process; dimer models; statistics; Invariance; crystal; GROWTH

摘要

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.