The Simple Exclusion Process as Seen from a Tagged Particle

Abstract

The simple exclusion process "as seen from a tagged particle" is studied. The set of translation invariant and invariant measures for this process is determined in the translation invariant case on $\mathbb{Z}^d$. The set of all invariant measures is determined in the nearest neighbor asymmetric case on $\mathbb{Z}$. The domains of attraction of the invariant measures are established in the one-dimensional nearest neighbor translation invariant case.