Absorbing-state phase transition in biased activated random walk
Abstract
We consider the activated random walk (ARW) model on , which undergoes a transition from an absorbing regime to a regime of sustained activity. In any dimension we prove that the system is in the active regime when the particle density is less than one, provided that the jump distribution is biased and that the sleeping rate is small enough. This answers a question from Rolla and Sidoravicius (2012) and Dickman, Rolla and Sidoravicius (2010) in the case of biased jump distribution. Furthermore, we prove that the critical density depends on the jump distribution.
Cite
@article{arxiv.1403.1986,
title = {Absorbing-state phase transition in biased activated random walk},
author = {Lorenzo Taggi},
journal= {arXiv preprint arXiv:1403.1986},
year = {2017}
}
Comments
In version 5, the upper bound for the critical density in high dimensions has been refined and it has been proved that the critical density depends on the jump distribution. Moreover, some steps of the proof have been simplified. in Electronic Journal of Probability (2016)