Random walks in dynamic random environment

Random motions in random media have been intensively studied for over forty years and many interesting features of these models have been discovered. The aim is to understand the motion of a particle in a turbulent media.

Most of the work has been focused on the case where the particle evolves in a static random environment, for which slow-downs and trapping phenomena have been proved.
More recently, mathematicians and physicists have been interested in the case of dynamic random environments, where the media can fluctuate with time. Random walks on the exclusion process is probably the canonical model for the field. Much less is known on this model, but exciting conjectures and questions have been made.

Some of the most challenging questions concern the possibility of super-diffusive regimes, and the existence of effective traps along the trajectory of the walk.

In this project, we aim at, on one hand, adapt the techniques recently developped in one dimension to the multi-dimensional model and, on the other hand, understand the presence or absence of atypical behaviors for this model.