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Point-to-line last passage percolation and the invariant measure of a system of reflecting Brownian motions
Version 2 2023-06-07, 08:44
Version 1 2023-06-07, 06:51
journal contribution
posted on 2023-06-07, 08:44 authored by William FitzGerald, Jon WarrenThis 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.
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- Published
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Probability Theory and Related FieldsISSN
0178-8051Publisher
Springer VerlagExternal DOI
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- Mathematics Publications
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- Yes
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2020-04-24First Open Access (FOA) Date
2020-04-24First Compliant Deposit (FCD) Date
2020-04-23Usage metrics
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