A Large deviation principle for last passage times in an asymmetric Bernoulli potential

TL;DR

This paper establishes a large deviation principle for last passage times in a Bernoulli environment, providing explicit formulas and analyzing the shape function's properties, including flat edges.

Contribution

It introduces an exactly solvable model with a Burke-type property and derives explicit rate functions and limiting log-moment generating functions.

Findings

Proved a large deviation principle for the model

Derived explicit rate functions and moment generating functions

Analyzed the shape function's flat edge behavior

Abstract

We prove a large deviation principle and give an expression for the rate function, for the last passage time in a Bernoulli environment. The model is exactly solvable and its invariant version satisfies a Burke-type property. Finally, we compute explicit limiting logarithmic moment generating functions for both the classical and the invariant models. The shape function of this model exhibits a flat edge in certain directions, and we also discuss the rate function and limiting log-moment generating functions in those directions.