On Fixation of Activated Random Walks

@inproceedings{Amir2009OnFO,
  title={On Fixation of Activated Random Walks},
  author={Gideon Amir and Ori Gurel-Gurevich},
  year={2009}
}
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… CONTINUE READING

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Activated Random Walkers: Facts

R. Dickman, L. T. Rolla, V. Sidoravicius
Conjectures and Challenges, Journal of Statistical Physics 138 • 2010
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