# Quenched large deviations for brownian motion in a random potential

## TL;DR

This paper establishes a quenched large deviation principle for Brownian motion in a broad class of stationary, non-negative potentials without regularity assumptions, extending previous results to potentials with polynomial decay.

## Contribution

It proves a quenched large deviation principle for Brownian motion in non-negative stationary potentials under minimal moment conditions, without requiring regularity.

## Key findings

- LDP holds for potentials with polynomial decay
- Applicable to classical and recent potentials
- No regularity assumptions needed

## Abstract

A quenched large deviation principle for Brownian motion in a non-negative, stationary potential is proved. A sufficient moment condition on the potential is given but unlike the results of Armstrong and Tran (2014) no regularity is assumed. The proof is based on a method developed by Sznitman (1994) for Brownian motion among Poissonian potential. In particular, the LDP holds for potentials with polynomially decaying correlations such as the classical potentials studied by L. Pastur (1977) and R. Fukushima (2008) and the potentials recently introduced by H. Lacoin (2012).