The simple exclusion process as seen from a tagged particle
The simple exclusion process ``as seen from a tagged particle'' is studied for particle configurations in \({\mathbb{Z}}^ d\) with translation invariant jump rates. Its existence is established and its translation invariant and invariant measures are determined. They are shown to be exactly the corresponding measures of the original process conditioned on the existence of a particle at the origin. In the one-dimensional nearest neighbour asymmetric case the set of all invariant measures is determined. In addition, to the corresponding conditioned measures of the original process, there exists a two-parameter family of extremal invariant measures with a finite number of particles to the left of the origin, if the process tends to the right. The study of this case is based on the known correspondence with the zero range process. Finally the domain of attraction of the invariant measures is determined in the one-dimensional nearest neighbour translation invariant case.
scientific article; zbMATH DE number 4022333