English

Diffusive bounds for the critical density of activated random walks

Probability 2019-07-31 v1 Mathematical Physics math.MP

Abstract

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

Cite

@article{arxiv.1907.12694,
  title  = {Diffusive bounds for the critical density of activated random walks},
  author = {Amine Asselah and Leonardo T. Rolla and Bruno Schapira},
  journal= {arXiv preprint arXiv:1907.12694},
  year   = {2019}
}
R2 v1 2026-06-23T10:34:19.703Z