Concentrations for the simple random walk in unbounded nonnegative potentials

Abstract

We consider the simple random walk in i.i.d. nonnegative potentials on the multidimensional cubic lattice. Our goal is to investigate the cost paid by the simple random walk for traveling from the origin to a remote location in a landscape of potentials. In particular, we obtain concentration inequalities for the travel cost in unbounded nonnegative potentials.

arXiv commentThis is the corrected version of the paper. We have deleted Section 5 because there is an error of the proof of Proposition 5.2 of the previous. 26 pages