How far do Activated Random Walkers spread from a single source?

Abstract

Unlike many particle systems, Activated Random Walk has nontrivial behavior even in one spatial dimension. We prove inner and outer bounds on the spread of n activated random walkers from a single source in Z. The inner bound involves a comparison with the stationary distribution of activated random walkers on a finite interval, while the outer bound involves a comparison with the stabilization of an infinite Bernoulli configuration of activated random walkers on Z.

26 pages, 5 figures

References in corpus (4)

• Sandpiles on the square lattice
• Activated Random Walks on ${\mathbb{Z}}^d$
• Activated Random Walks
• Density relaxation in conserved Manna sandpiles

Cited by in corpus (1)

• Exact sampling and fast mixing of Activated Random Walk