Large deviations for random walk in random environment

We will consider a one-dimensional random walk in random environment. After a brief recap of the state of the art concerning the limiting behaviour of the precess in question we will show how to improve large deviation results established previously by Y. Peres, A. Dembo and O. Zeituni ”Tail estimates for one-dimensional random walk in random environment”, Comm. Math. Phys, 1996. The talk is based on a joint work with D. Buraczewski available at https://arxiv.org/abs/1710.01075.

Keywords: random walk, random environment, first passage time, branching process with immigration, precise large deviations.