Interacting particle systems and homogenization

An important example of an interacting particle system is the exclusion process. It consists of particles performing simple random walks on Z^d, with the rule that any attempted jump of one particle onto another is suppressed.

The talk will start with a more precise definition and construction of this process, and a derivation of some of its basic properties. Next, we will paint one of the particles red and follow its trajectory. It is known that the trajectory of this red particle "homogenizes", in the sense that it looks like a Brownian motion over large scales. We will discuss quantitative versions of this statement, which are for the most part open questions.