The hockey-stick conjecture for activated random walk

Proceedings of the American Mathematical Society 2026 Open access

Read full text
Authors: Christopher Hoffman, Tobias Johnson, Matthew Junge
DOI: 10.1090/proc/17656
Cited by: 0
References: 22

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.

Fields of Study & Subjects

Hydrocarbon exploration and reservoir analysis Enhanced Oil Recovery Techniques Hydraulic Fracturing and Reservoir Analysis

Publication details

Journal / source
Proceedings of the American Mathematical Society
Volume
154
Issue
8
Pages
3553–3566
Publication date
4 February 2026
Language
EN