Limit theorems for the tagged particle in exclusion processes on regular trees

We consider exclusion processes on a rooted $d$-regular tree. We start from a Bernoulli product measure conditioned on having a particle at the root, which we call the tagged particle. For $d > 2$, we show that the tagged particle has positive linear speed and satisfes a central limit theorem. We give an explicit formula for the speed. As a key step in the proof, we first show that the exclusion process “seen from the tagged particle” has an ergodic invariant measure. The talk is based on a joint paper with Peng Chen, Nina Gantert, Dominik Schmid.