Active Phase for Activated Random Walk on Z

2020/09/20 by Hoffman, Christopher, Richey, Jacob, Rolla, Leonardo T.
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2009.09491

Abstract

We consider the Activated Random Walk model on ℤ. In this model, each particle performs a continuous-time simple symmetric random walk, and falls asleep at rate λ. A sleeping particle does not move but it is reactivated in the presence of another particle. We show that for any sleep rate λ< ∞ if the density ζ is close enough to 1 then the system stays active.

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