The hockey-stick conjecture for activated random walk
Probability
2026-03-25 v4 Statistical Mechanics
Abstract
We prove a conjecture of Levine and Silvestri that the driven-dissipative activated random walk model on an interval drives itself directly to and then sustains a critical density. This marks the first rigorous confirmation of a sandpile model behaving as in Bak, Tang, and Wiesenfeld's original vision of self-organized criticality.
Keywords
Cite
@article{arxiv.2411.02541,
title = {The hockey-stick conjecture for activated random walk},
author = {Christopher Hoffman and Tobias Johnson and Matthew Junge},
journal= {arXiv preprint arXiv:2411.02541},
year = {2026}
}
Comments
13 pages; minor changes in response to referees' comments