Large deviations for one-dimensional random walks on discrete point processes

Berger and Rosenthal introduced a random walk model on discrete point processes, that is, a simple random walk defined on a random subset of Z(d). In this article, we study both the quenched and the annealed large deviations for the one-dimensional case. Their rate functions are linked via a variational formula, analogous to the classical one-dimensional random walk in random environment. (C) 2014 Elsevier B.V. All rights reserved.