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

	PDF - Accepted Version Restricted to SRO admin only Download (301kB)
	PDF - Published Version Available under License Creative Commons Attribution. Download (721kB)

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

View download statistics for this item

📧 Request an update