Upper Bound for the Critical Density of Biased Activated Random Walk
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Submission date: 20. Mar. 2014 (revised version: March 2014)
MSC-Numbers: 82C22, 82C26
Keywords and phrases: Activated Random Walk, Out-of-Equilibrium Phase Transition, Interacting Particle System
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We provide a new upper bound for the critical density of Activated Random Walk in case of biased distribution of jumps. With finite sleeping rate the bound is strictly less than one in one dimension for all initial particles distribution and in higher dimension for some initial particles distributions. This answers a question from Dickman, Rolla and Sidoravicius (2010) in case of bias.