2019/04/05 by Will FitzGerald, FitzGerald, Will, Jon Warren +1
Computer Science · Mathematics · #60B20 #60J65 #60K35 #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math.PR #msc:60B20 #msc:60J65 #msc:60K35
paper · pdf · doi:10.48550/arxiv.1904.03253
41 pages, proofs in Section 4.1 rewritten and minor changes to presentation
openalex publication_date 2019/04/05 · arxiv created 2019/07/16 · arxiv updated 2019/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.