The hockey-stick conjecture for activated random walk

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

References in corpus (10)

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