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In this article, we prove a lower bound for the fluctuations of symmetricrandom walks on dynamic random environments in dimension $1 + 1$ in theperturbative regime where the walker is weakly influenced by the environment.We suppose that the random environment is invariant with respect totranslations and reflections, satisfies the FKG inequality and a mild mixingcondition. The techniques employed are inspired by percolation theory,including a Russo-Seymour-Welsh (RSW) inequality. To exemplify the generalityof our results, we provide two families of fields that satisfy our hypotheses:a class of Gaussian fields and Confetti percolation models.

Fluctuation bounds for symmetric random walks on dynamic environments via Russo-Seymour-Welsh