Quenched invariance principle for biased random walks in random conductances in the sub-ballistic regime

Abstract

We consider a biased random walk in positive random conductances on ${\mathbb{Z}}^d$ for $d\ge 5$. In the sub-ballistic regime, we prove the quenched convergence of the properly rescaled random walk towards a Fractional Kinetics.

59 pages, 8 figures. Final version