The speed of biased random walks among dynamical random conductances

Abstract

We study biased variable-speed random walks in dynamical random conductances. Assuming that the conductances are upper-bounded, we prove that the walk has strictly positive speed for every bias $\lambda>0$. We then give an explicit asymptotic formula for the speed for $\lambda \to + \infty$, and prove two monotonicity properties for the speed. Finally, we provide an example showing that, even for conductances that are bounded and bounded away from zero, the speed can be asymptotically decreasing in the bias.