Open Access
2010 On Fixation of Activated Random Walks
Ori Gurel-Gurevich, Gideon Amir
Author Affiliations +
Electron. Commun. Probab. 15: 119-123 (2010). DOI: 10.1214/ECP.v15-1536


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, in a more general setting then had been previously known (by Shellef).


Download Citation

Ori Gurel-Gurevich. Gideon Amir. "On Fixation of Activated Random Walks." Electron. Commun. Probab. 15 119 - 123, 2010.


Accepted: 26 April 2010; Published: 2010
First available in Project Euclid: 6 June 2016

zbMATH: 1231.60110
MathSciNet: MR2643591
Digital Object Identifier: 10.1214/ECP.v15-1536

Primary: 60K35
Secondary: 82C22

Keywords: Activated Random Walks , Interacting particles system

Back to Top