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