The Annals of Probability

Duality between coalescence times and exit points in last-passage percolation models

Leandro P. R. Pimentel

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In this article, we prove a duality relation between coalescence times and exit points in last-passage percolation models with exponential weights. As a consequence, we get lower bounds for coalescence times, with scaling exponent $3/2$, and we relate its distribution with variational problems involving the Brownian motion process and the Airy$_{2}$ process. The proof relies on the relation between Busemann functions and the Burke property for stationary versions of the last-passage percolation model with boundary.

Article information

Ann. Probab., Volume 44, Number 5 (2016), 3187-3206.

Received: November 2013
Revised: May 2015
First available in Project Euclid: 21 September 2016

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Zentralblatt MATH identifier

Primary: 60C05: Combinatorial probability 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60F05: Central limit and other weak theorems

Last passage percolation directional geodesics coalescence scaling limit


Pimentel, Leandro P. R. Duality between coalescence times and exit points in last-passage percolation models. Ann. Probab. 44 (2016), no. 5, 3187--3206. doi:10.1214/15-AOP1044.

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