We prove that random walks in random environments, that are exponentially mixing in space and time, are almost surely diffusive, in the sense that their scaling limit is given by the Wiener measure.
Bricmont, J., & Kupiainen, A. (2009). Random Walks in Space Time Mixing Environments. Journal of Statistical Physics, 134(5-6), 979-1004. https://doi.org/10.1007/s10955-009-9689-1 (Original work published 2009)