Diffusive bounds for the critical density of activated random walks

Amine Asselah, Leonardo T. Rolla, Bruno Schapira

Published 2019-07-30Version 1

We consider symmetric activated random walks on $\mathbb{Z}$, and show that the critical density $\zeta_c$ satisfies $c\sqrt{\lambda} \leq \zeta_c(\lambda) \leq C \sqrt{\lambda}$ where $\lambda$ denotes the sleep rate.