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- Title
Point-to-line last passage percolation and the invariant measure of a system of reflecting Brownian motions.
- Authors
FitzGerald, Will; Warren, Jon
- 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.
- Subjects
BROWNIAN motion; INVARIANT measures; WIENER processes; PERCOLATION; PARTITION functions; RANDOM matrices
- Publication
Probability Theory & Related Fields, 2020, Vol 178, Issue 1/2, p121
- ISSN
0178-8051
- Publication type
Article
- DOI
10.1007/s00440-020-00972-z