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September 2016 Duality between coalescence times and exit points in last-passage percolation models
Leandro P. R. Pimentel
Ann. Probab. 44(5): 3187-3206 (September 2016). DOI: 10.1214/15-AOP1044

Abstract

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.

Citation

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Leandro P. R. Pimentel. "Duality between coalescence times and exit points in last-passage percolation models." Ann. Probab. 44 (5) 3187 - 3206, September 2016. https://doi.org/10.1214/15-AOP1044

Information

Received: 1 November 2013; Revised: 1 May 2015; Published: September 2016
First available in Project Euclid: 21 September 2016

zbMATH: 1361.60095
MathSciNet: MR3551194
Digital Object Identifier: 10.1214/15-AOP1044

Subjects:
Primary: 60C05, 60K35
Secondary: 60F05

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.44 • No. 5 • September 2016
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