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 -