TIME-TIME COVARIANCE FOR LAST PASSAGE PERCOLATION IN HALF-SPACE

• 成果类型: Article
• 署名作者: Ferrari, Patrik; Occelli, Alessandra
• 署名单位: University of Bonn; Universite d'Angers
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP1974
• 发表日期: 2024
• 页码: 627-674
• 关键词: fluctuations; limit; tasep; UNIVERSALITY; asymptotics

摘要

This article studies several properties of the half-space last passage percolation, in particular the two-time covariance. We show that, when the two end-points are at small macroscopic distance, then the first-order correction to the covariance for the point-to-point model is the same as the one of the stationary model. In order to obtain the result, we first derive comparison inequalities of the last passage increments for different models. This is used to prove tightness of the point-to-point process as well as localization of the geodesics. Unlike for the full-space case, for half-space we have to overcome the difficulty that the point-to-point model in half-space with generic start and end-points is not known.