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

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.