Large deviations for Brownian motion in a random potential

Abstract

A quenched large deviation principle for Brownian motion in a stationary potential is proved. As the proofs are based on a method developed by Sznitman [Comm. Pure Appl. Math. 47 (1994) 1655–1688] for Brownian motion among obstacles with compact support no regularity conditions on the potential is needed. In particular, the sufficient conditions are verified by potentials with polynomially decaying correlations such as the classical potentials studied by Pastur [Teoret. Mat. Fiz. 32 (1977) 88–95] and Fukushima [J. Stat. Phys. 133 (2008) 639–657] and the potentials recently introduced by Lacoin [Ann. Inst. Henri Poincaré Probab. Stat. 48 (2012) 1010–1028; 1029–1048].