A Driven Tagged Particle in Symmetric Exclusion Processes with Removals

TL;DR

This paper studies the movement of a driven tagged particle in a symmetric exclusion process with particle removals, establishing limit theorems and characterizing ergodic measures using martingale and regenerative techniques.

Contribution

It introduces a novel analysis of a driven tagged particle with removal rules, providing limit theorems and ergodic measure characterization in this setting.

Findings

Proved law of large numbers for the tagged particle displacement

Established a central limit theorem for the process

Derived a large deviation principle for the displacement

Abstract

We consider a driven tagged particle in a symmetric exclusion process on Z with a removal rule. In this process, untagged particles are removed once they jump to the left of the tagged particle. We investigate the behavior of the displacement of the tagged particle and prove limit theorems of it: an (annealed) law of large numbers, a central limit theorem, and a large deviation principle. We also characterize a class of ergodic measures for the environment process. Our approach is based on analyzing two auxiliary processes with associated martingales and a regenerative structure.