A Driven Tagged Particle in Asymmetric Exclusion Processes

TL;DR

This paper studies a driven tagged particle in an asymmetric exclusion process, revealing conditions for ballistic behavior and invariant measures, using coupling, martingale methods, and current analysis.

Contribution

It introduces a model with a driven tagged particle having different jump rates, demonstrating ballistic behavior and invariant measures in asymmetric exclusion processes.

Findings

Tagged particle exhibits ballistic behavior under certain jump rate conditions.

Existence of non-trivial invariant measures for the environment process.

Analysis techniques include coupling, martingale approach, and current analysis.

Abstract

We consider the asymmetric exclusion process with a driven tagged particle on Z which has different jump rates from other particles and show that the tagged particle can have a ballistic behavior when the non-tagged particles have non-nearest-neighbor jump rates. We show the existence of some non-trivial invariant measures for the environment process viewed from the tagged particle. Our arguments are based on coupling, the martingale approach, and analyzing currents through fixed bonds.