2020.06.25 M. Hilário - Random walks on dynamical random environments with non-uniform mixing (2/2)
Channel: One World Probability
Date: 2020-06-25

In these two consecutive talks we will discuss recent results on the
limiting behavior of random walks on dynamical random environments. The
strength of these results depends a great deal on space-time mixing properties
imposed to the environment but also on other features like the dimension and
the allowed transitions. In our case, we restrict ourselves to random walks
evolving on one-dimensional random environments given by conservative
interacting particle systems such as the simple symmetric exclusion process.
For this setting, conservation of particles leads to poor-mixing conditions
which complicates the applicability of some available tools. Our goal is to
explain how renormalization can be used to handle these difficulties in order
to obtain law of large numbers, large deviation estimates. The first talk will
be a non-technical introduction to the subject. In the second talk, we provide
a more detailed idea of how to prove the results.

All the results were obtained on several joint works with Oriane Blondel,

Frank den Hollander, Daniel Kious, Renato dos Santos and Vladas Sidoravicius.


The first talk will be a non-technical introduction to the subject.