Process-level quenched large deviations for random walk in random environment

TL;DR

This paper establishes a level 3 large deviation principle for bounded step size random walks in ergodic random environments, linking the rate function to relative entropy, applicable across arbitrary dimensions.

Contribution

It extends large deviation principles to process-level analysis for random walks in random environments with ellipticity, in any dimension.

Findings

Proves a level 3 large deviation principle for the process.

Connects the rate function to relative entropy.

Applicable to ergodic environments with bounded steps.

Abstract

We consider a bounded step size random walk in an ergodic random environment with some ellipticity, on an integer lattice of arbitrary dimension. We prove a level 3 large deviation principle, under almost every environment, with rate function related to a relative entropy.