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

We consider a biased random walk in positive random conductances on $\mathbb{Z}^d$ for $d\geq 5$. In the sub-ballistic regime, we prove the quenched convergence of the properly rescaled random walk towards a Fractional Kinetics.Comment: 59 pages, 8 figures. Modifications in Theorem 1.2, Section 3-4-