Point-to-line last passage percolation and the invariant measure of a system of reflecting Brownian motions

• 成果类型: Article
• 署名作者: FitzGerald, Will; Warren, Jon
• 署名单位: University of Sussex; University of Warwick
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-020-00972-z
• 发表日期: 2020
• 页码: 121-171
• 关键词: free-energy fluctuations; largest-eigenvalue; directed polymers; ensembles; GROWTH

摘要

This paper proves an equality in law between the invariant measure of a reflected system of Brownian motions and a vector of point-to-line last passage percolation times in a discrete random environment. A consequence describes the distribution of the all-time supremum of Dyson Brownian motion with drift. A finite temperature version relates the point-to-line partition functions of two directed polymers, with an inverse-gamma and a Brownian environment, and generalises Dufresne's identity. Our proof introduces an interacting system of Brownian motions with an invariant measure given by a field of point-to-line log partition functions for the log-gamma polymer.