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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, 78 . pp. 121-171. 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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| 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: |
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| Date of first compliant deposit: | 16 April 2020 | ||||||||
| Volume: | 78 | ||||||||
| Page Range: | pp. 121-171 | ||||||||
| 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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