Electronic Journal of Probability

Absorbing-state phase transition in biased activated random walk

Lorenzo Taggi

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We consider the activated random walk model on $\mathbb{Z} ^d$, which undergoes a transition from an absorbing regime to a regime of sustained activity. A central question for this model involves the estimation of the critical density $\mu _c$. We prove that if the jump distribution is biased, then $\mu _c < 1$ for any sleeping rate $\lambda $, $d \geq 1$, and that $\mu _c \to 0$ as $\lambda \to 0$ in one dimension. 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.

Article information

Electron. J. Probab. Volume 21, Number (2016), paper no. 13, 15 pp.

Received: 30 April 2015
Accepted: 27 January 2016
First available in Project Euclid: 23 February 2016

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Digital Object Identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82C22: Interacting particle systems [See also 60K35]

interacting particles activated random walk lattice gasses Abelian networks

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Taggi, Lorenzo. Absorbing-state phase transition in biased activated random walk. Electron. J. Probab. 21 (2016), paper no. 13, 15 pp. doi:10.1214/16-EJP4275. https://projecteuclid.org/euclid.ejp/1456246244.

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