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

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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, 178 . pp. 121-171. doi:10.1007/s00440-020-00972-z

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Official URL: https://doi.org/10.1007/s00440-020-00972-z

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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: Journal Article
Alternative Title:
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH): Brownian motion processes , Random matrices
Journal or Publication Title: Probability Theory and Related Fields
Publisher: Springer
ISSN: 0178-8051
Official Date: October 2020
Dates:
DateEvent
October 2020Published
17 April 2020Available
28 March 2020Accepted
Volume: 178
Page Range: pp. 121-171
DOI: 10.1007/s00440-020-00972-z
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
EP/HO23364/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
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