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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 . doi:10.1007/s00440-020-00972-z (In Press)
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Official URL: https://doi.org/10.1007/s00440-020-00972-z
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 | ||||||
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| 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: | 17 April 2020 | ||||||
| Dates: |
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| Date of first compliant deposit: | 16 April 2020 | ||||||
| DOI: | 10.1007/s00440-020-00972-z | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | In Press | ||||||
| Access rights to Published version: | Open Access | ||||||
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