Invariance principle for `push' tagged particles for a Toom Interface

TL;DR

This paper proves an invariance principle for push-tagged particles in a non-reversible one-dimensional Toom model, showing they move diffusively with a slower speed than second-class particles, expanding understanding of particle dynamics.

Contribution

It introduces a new invariance principle for push-tagged particles in the non-reversible Toom model, a case previously not covered by existing techniques.

Findings

Push-tagged particles move diffusively with a slower rate than second-class particles.

The invariance principle applies specifically to the non-reversible one-dimensional Toom model.

The result extends the class of processes where invariance principles are established.

Abstract

In many interacting particle systems, tagged particles move diffusively upon subtracting a drift. General techniques to prove such `invariance principles' are available for reversible processes (Kipnis-Varadhan) and for non-reversible processes in dimension $d>2$. The interest of our paper is that it considers a non-reversible one-dimensional process: the Toom model. The reason that we can prove the invariance principle is that in this model, push-tagged particles move manifestly slower than second-class particles.