Point-to-line last passage percolation and the invariant measure of a system of reflecting Brownian motions
2020 ◽
Vol 178
(1-2)
◽
pp. 121-171
Keyword(s):
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.
2000 ◽
Vol 32
(01)
◽
pp. 177-192
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Keyword(s):
2000 ◽
Vol 32
(1)
◽
pp. 177-192
◽
Keyword(s):
2010 ◽
Vol 10
(03)
◽
pp. 315-339
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1996 ◽
Vol 28
(04)
◽
pp. 1145-1176
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Keyword(s):