UNIVERSALITY OF THE GEODESIC TREE IN LAST PASSAGE PERCOLATION

• 成果类型: Article
• 署名作者: Busani, Ofer; Ferrari, Patrik L.
• 署名单位: University of Bristol; University of Bonn
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/21-AOP1530
• 发表日期: 2022
• 页码: 90-130
• 关键词: growth-models; fluctuations; tasep; distributions; subsequences; asymptotics; Coalescence; interfaces; polymers; png

摘要

In this paper, we consider the geodesic tree in exponential last passage percolation. We show that for a large class of initial conditions around the origin, the line-to-point geodesic that terminates in a cylinder located around the point (N, N), and whose width and length are o(N-2/3) and o(N), respectively, agrees in the cylinder, with the stationary geodesic sharing the same end-point. In the case of the point-to-point model where the geodesic starts from the origin, we consider width delta N-2/3, length up to delta(3/2) N/(log(delta(-1)))(3), and provide lower and upper bounds for the probability that the geodesics agree in that cylinder.