Quenched Large Deviations for Random Walk in a Random Environment

We take the point of view of a particle performing random walk with bounded jumps on Z(d) in a stationary and ergodic random environment. We prove the quenched large-deviation principle (LDP) for the pair empirical measure of the so-called environment Markov chain. By an appropriate contraction, we deduce the quenched LDP for the mean velocity of the particle and obtain a variational formula for the corresponding rate function. We propose an ansatz for the minimizer of this formula. When d = 1, we verify this ansatz and generalize the nearest-neighbor result of Comets, Gantert, and Zeitouni to walks with bounded jumps. (C) 2009 Wiley Periodicals, Inc.