In this talk we will review a few general statements about Random Walks on Dynamic Random Environments (RWDRE). As expected, if the random environment satisfies stronger mixing conditions, more can be said about the behavior of the random walk. Then we will focus on a recent work establishing lower bounds on fluctuations for certain RWDRE models. This result requires the environment to be symmetric, satisfy the FKG inequality as well as a mixing condition. The techniques employed in the proof are inspired by percolation theory and the Russo-Seymour-Welsh (RSW) inequality. We finally exemplify our main result with two examples of environments: a class of Gaussian fields and a Confetti percolation medium.
