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2016 Absorbing-state phase transition in biased activated random walk
Lorenzo Taggi
Electron. J. Probab. 21: 1-15 (2016). DOI: 10.1214/16-EJP4275

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.

Citation

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Lorenzo Taggi. "Absorbing-state phase transition in biased activated random walk." Electron. J. Probab. 21 1 - 15, 2016. https://doi.org/10.1214/16-EJP4275

Information

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

zbMATH: 1336.60195
MathSciNet: MR3485355
Digital Object Identifier: 10.1214/16-EJP4275

Subjects:
Primary: 60K35, 82C22

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Vol.21 • 2016
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