Speaker: Marcelo Hilario - UFMG

Title: Random walks on dynamic random environments with non-uniform mixing.

Abstract: In this talk, we will discuss recent results on the limiting behavior of random walks in dynamic random environments. We will mainly discuss the case when the random walk evolves on one-dimensional random environments given by conservative interacting particle systems such as the simple symmetric exclusion process. Its transitions probabilities will depend on the current occupation environment nearby. Conservation of particles leads to poor mixing conditions and we explain how renormalization techniques can be useful to obtain the law of large numbers, large deviation estimates, and sometimes central limit theorems. The talk is based on several joint works with Oriane Blondel, Frank den Hollander, Daniel Kious, Renato dos Santos, Vladas Sidoravicius and Augusto Teixeira.