# Seminário de Análise, Geometria e Sistemas Dinâmicos

### Invariance principle for a slowed random walk driven by symmetric exclusion

Joint work with Milton Jara.

We establish an invariance principle for a random walk driven by the symmetric exclusion process in one dimension. The walk has a drift to the left (resp. right) when it sits on a particle (resp. hole). The environment starts from equilibrium and is speeded up with respect to the walker. After a suitable space-time rescaling, the random walk converges to a sum of a Brownian motion and a Gaussian process with stationary increments, independent of the Brownian motion. Our main tool in the proof is an estimate on the relative entropy between the law of the environment process and the equilibrium measure of the exclusion process.