ASYMPTOTIC DOMINO STATISTICS IN THE AZTEC DIAMOND

• 成果类型: Article
• 署名作者: Chhita, Sunil; Johansson, Kurt; Young, Benjamin
• 署名单位: University of Bonn; Royal Institute of Technology; University of Oregon
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1021
• 发表日期: 2015
• 页码: 1232-1278
• 关键词: local statistics; tilings; lattice; dimers; limit

摘要

We study random domino filings of the Aztec diamond with different weights for horizontal and vertical dominoes. A domino tiling of an Aztec diamond can also be described by a particle system which is a determinantal process. We give a relation between the correlation kernel for this process and the inverse Kasteleyn matrix of the Aztec diamond. This gives a formula for the inverse Kasteleyn matrix which generalizes a result of Helfgott. As an application, we investigate the asymptotics of the process formed by the southern dominoes close to the frozen boundary. We find that at the northern boundary, the southern domino process converges to a thinned Airy point process. At the southern boundary, the process of holes of the southern domino process converges to a multiple point process that we call the thickened Airy point process. We also study the convergence of the domino process in the unfrozen region to the limiting Gibbs measure.