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

TL;DR

This paper establishes a duality relation in last-passage percolation models with exponential weights, linking coalescence times and exit points, and derives bounds and distributional relations involving Brownian motion and the Airy process.

Contribution

It introduces a duality between coalescence times and exit points in last-passage percolation, providing new bounds and connections to stochastic processes.

Findings

Lower bounds for coalescence times with exponent 3/2

Distributional relations involving Brownian motion and Airy process

Duality relation between coalescence times and exit points

Abstract

In this paper 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 process.