Local stationarity in exponential last-passage percolation
成果类型：
Article
署名作者：
Balazs, Marton; Busani, Ofer; Seppalainen, Timo
署名单位：
University of Bristol; University of Wisconsin System; University of Wisconsin Madison
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-021-01035-7
发表日期：
2021
页码：
113-162
关键词：
摘要：
We consider point-to-point last-passage times to every vertex in a neighbourhood of size delta N-2/3 at distance N from the starting point. The increments of the last-passage times in this neighbourhood are shown to be jointly equal to their stationary versions with high probability that depends only on delta. Through this result we show that (1) the Airy(2) process is locally close to a Brownian motion in total variation; (2) the tree of point-to-point geodesics from every vertex in a box of side length delta N-2/3 going to a point at distance N agrees inside the box with the tree of semi-infinite geodesics going in the same direction; (3) two point-to-point geodesics started at distance N-2/3 from each other, to a point at distance N, will not coalesce close to either endpoint on the scale N. Our main results rely on probabilistic methods only.
来源URL：