The simple exclusion process as seen from a tagged particle
type: Item
instance of: scholarly article
title: The simple exclusion process as seen from a tagged particle
zbMATH Open document ID: 0628.60103
published in: The Annals of Probability
publication date: 1986-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 4022333
zbMATH Keywords: simple exclusion process
zbMATH Keywords: tagged particle
zbMATH Keywords: invariant measures
zbMATH Keywords: extremal invariant measures
zbMATH Keywords: zero range process
author: Pablo A. Ferrari
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992369
OpenAlex ID: W2069575748
DOI: 10.1214/AOP/1176992369
description: scientific article; zbMATH DE number 4022333