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
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