## Abstract

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. In particular, we do not require the particles path distribution to be Markovian. This allows us to answer a question of Rolla and Sidoravicius [3,4], in a more general setting then had been previously known (by Shellef [5]).

Original language | American English |
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Pages (from-to) | 119-123 |

Number of pages | 5 |

Journal | Electronic Communications in Probability |

Volume | 15 |

DOIs | |

State | Published - 1 Jan 2010 |

Externally published | Yes |

## Keywords

- Activated Random Walks
- Interacting Particles System