TY - JOUR

T1 - On fixation of activated random walks

AU - Amir, Gideon

AU - Gurel-Gurevich, Ori

PY - 2010/1/1

Y1 - 2010/1/1

N2 - 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]).

AB - 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]).

KW - Activated Random Walks

KW - Interacting Particles System

UR - http://www.scopus.com/inward/record.url?scp=84963846574&partnerID=8YFLogxK

U2 - 10.1214/ECP.v15-1536

DO - 10.1214/ECP.v15-1536

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AN - SCOPUS:84963846574

SN - 1083-589X

VL - 15

SP - 119

EP - 123

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

ER -