  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.
