## Electronic Journal of Probability

### Absorbing-state phase transition in biased activated random walk

Lorenzo Taggi

#### Abstract

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

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

Dates
Accepted: 27 January 2016
First available in Project Euclid: 23 February 2016

https://projecteuclid.org/euclid.ejp/1456246244

Digital Object Identifier
doi:10.1214/16-EJP4275

#### Citation

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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