paper

The hockey-stick conjecture for activated random walk

arXiv:2411.02541 · doi:10.1090/proc/17656

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.

13 pages; minor changes in response to referees' comments

The hockey-stick conjecture for activated random walk · wovepaper