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

FitzGerald, Will and Warren, Jon (2020) Point-to-line last passage percolation and the invariant measure of a system of reflecting Brownian motions. Probability Theory and Related Fields. ISSN 0178-8051

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Abstract

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.

Item Type: Article
Keywords: Reflected Brownian motions, Random matrices, Dufresne’s identity, Log-gamma polymer, Point-to-line last passage percolation
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
SWORD Depositor: Mx Elements Account
Depositing User: Mx Elements Account
Date Deposited: 24 Apr 2020 07:50
Last Modified: 24 Apr 2020 08:00
URI: http://sro.sussex.ac.uk/id/eprint/91005

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