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

Probability 2021-11-17 v2

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.

Keywords

Cite

@article{arxiv.2011.02535,
  title  = {How far do Activated Random Walkers spread from a single source?},
  author = {Lionel Levine and Vittoria Silvestri},
  journal= {arXiv preprint arXiv:2011.02535},
  year   = {2021}
}

Comments

26 pages, 5 figures

R2 v1 2026-06-23T19:55:24.883Z