On Fixation of Activated Random Walks

Understand

We prove that for the Activated Random Walks model on transitive unimodular graphs, if there is fixation, then every particle eventually fixates, almost surely.

• We deduce that the critical density is at most 1.
• Our methods apply for much more general processes on unimodular graphs.
• Roughly put, our result apply whenever the path of each particle has an automorphism invariant distribution and is independent of other particles' paths, and the interaction between particles is automorphism invariant and local.