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.
"Scaling limits for sub-ballistic biased random walks in random conductances." Ann. Probab. 46 (2) 605 - 686, March 2018. https://doi.org/10.1214/16-AOP1159