On the slow phase for fixed-energy Activated Random Walks
Probability
2026-04-09 v3
Abstract
We study the Activated Random Walk model on the one-dimensional ring, in the high density regime. We develop a toppling procedure that gradually builds an environment that can be used to show that activity will be sustained for a long time. This yields a self-contained and relatively short proof of existence of a slow phase for arbitrarily large sleep rates.
Cite
@article{arxiv.2408.07049,
title = {On the slow phase for fixed-energy Activated Random Walks},
author = {Bernardo N. B. de Lima and Leonardo T. Rolla and Célio Terra},
journal= {arXiv preprint arXiv:2408.07049},
year = {2026}
}