LOCAL GEOMETRY OF THE ROUGH-SMOOTH INTERFACE IN THE TWO-PERIODIC AZTEC DIAMOND

• 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); Durham University; Royal Institute of Technology
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1701
• 发表日期: 2022
• 页码: 974-1017
• 关键词: domino tilings; statistics

摘要

Random tilings of the two-periodic Aztec diamond contain three macroscopic regions: frozen, where the tilings are deterministic; rough, where the correlations between dominoes decay polynomially; smooth, where the correlations between dominoes decay exponentially. In a previous paper, the authors found that a certain averaging of height function differences at the rough-smooth interface converged to the extended Airy kernel point process. In this paper, we augment the local geometrical picture at this interface by introducing well-defined lattice paths which are closely related to the level lines of the height function. We show, after suitable centering and rescaling, that a point process from these paths converge to the extended Airy kernel point process provided that the natural parameter associated to the two-periodic Aztec diamond is small enough.