Active Phase for Activated Random Walk on Z

Abstract

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

29 pages, 2 figures

References in corpus (1)

• Activated Random Walks on ${\mathbb{Z}}^d$

Cited by in corpus (2)

• The hockey-stick conjecture for activated random walk
• Macroscopic flow out of a segment for Activated Random Walks in dimension 1