Scaling limits for sub-ballistic biased random walks in random conductances

Abstract

We consider biased random walks in positive random conductances on the $d$-dimensional lattice in the zero-speed regime and study their scaling limits. We obtain a functional law of large numbers for the position of the walker, properly rescaled. Moreover, we state a functional central limit theorem where an atypical process, related to the fractional kinetics, appears in the limit.