Edge statistics for lozenge tilings of polygons, I: concentration of height function on strip domains

• 成果类型: Article
• 署名作者: Huang, Jiaoyang
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-023-01238-0
• 发表日期: 2024
• 页码: 337-485
• 关键词: nonintersecting paths; general beta; UNIVERSALITY; RIGIDITY; fluctuations; asymptotics; eigenvalues; BOUNDARY; THEOREM

摘要

In this paper we study uniformly random lozenge tilings of strip domains. Under the assumption that the limiting arctic boundary has at most one cusp, we prove a nearly optimal concentration estimate for the tiling height functions and arctic boundaries on such domains: with overwhelming probability the tiling height function is within n(delta) of its limit shape, and the tiling arctic boundary is within n(1/3+delta) to its limit shape, for arbitrarily small delta > 0. This concentration result will be used in Aggarwal and Huang (Edge statistics for lozenge tilings of polygons, II: Airy line ensemble, 2021. arXiv:2108.12874) to prove that the edge statistics of simply-connected polygonal domains, subject to a technical assumption on their limit shape, converge to the Airy line ensemble.