On the continuity of Lyapunov exponents of random walk in random potential

Abstract

We consider a simple random walk in an i.i.d. nonnegative potential on the $d$-dimensional cubic lattice $\mathbb{Z}^{d}$, $d\geq3$. We prove that the Lyapunov exponents are continuous with respect to the law of the potential. In the quenched case, we assume that the potentials are integrable whilst there are no additional conditions in the annealed case.