We take the point of view of a particle performing random walk with bounded jumps on Z in a stationary and ergodic random environment. We prove the quenched large deviation principle (LDP) for the pair empirical measure of the 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 corresp...

Abstract. In his 2003 paper, Varadhan proves the averaged large deviation principle (LDP) for the mean velocity of a particle performing random walk in a random environment (RWRE) on Z with d ≥ 1, and gives a variational formula for the corresponding rate function Ia. Under the non-nestling assumption (resp. Kalikow’s condition), we show that Ia is strictly convex and analytic on a non-empty op...

Ceci est le troisième d’une série d’articles dans lesquels nous considérons une marche aléatoire unidimensionnelle un milieu refroidissant (MAMAR). Ce processus obtenu en partant (MAMA) et rafraîchissant l’environnement long séquence de temps déterministes, appelée rafraîchissement. Dans présent article, explorons deux questions pour des moments rafraîchissement généraux. Tout d’abord, examinon...

One dimensional excited random walk has been extensively studied for bounded, i.i.d. cookie environments. In this case, many important properties of the walk including transience or recurrence, positivity or non-positivity of the speed, and the limiting distribution of the position of the walker are all characterized by a single parameter δ, the total expected drift per site. In the more genera...