Large deviations for directed percolation on a thin rectangle

TL;DR

This paper establishes large deviation principles for a directed last-passage percolation model on a thin rectangle, extending previous results to subexponential weight distributions using Brownian embedding and KMT approximation.

Contribution

It extends large deviation results for directed percolation to subexponential weights, complementing prior Gaussian and finite-moment cases, via Brownian embedding techniques.

Findings

Large deviation principles are proven for Gaussian weights.

Results are extended to subexponential weight distributions.

The approach relies on Brownian path embedding and KMT approximation.

Abstract

Following the recent investigations of Baik and Suidan in \cite{baik2005gcl} and Bodineau and Martin in \cite{bodineau2005upl}, we prove large deviation properties for a last-passage percolation model in $\mathbb{Z}^{2}_{+}$ whose paths are close to the axis. The results are mainly obtained when the random weights are Gaussian or have a finite moment-generating function and rely, as in \cite{baik2005gcl} and \cite{bodineau2005upl}, on an embedding in Brownian paths and the KMT approximation. The study of the subexponential case completes the exposition.