On fixation of activated random walks

Gideon Amir, Ori Gurel-Gurevich

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

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 languageAmerican English
Pages (from-to)119-123
Number of pages5
JournalElectronic Communications in Probability
Volume15
DOIs
StatePublished - 1 Jan 2010
Externally publishedYes

Keywords

  • Activated Random Walks
  • Interacting Particles System

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