The hockey-stick conjecture for activated random walk

2024/11/04 by Christopher Hoffman, Hoffman, Christopher, Tobias Johnson +3 · 2 citations
Engineering · #60K35 #82C22 #Enhanced Oil Recovery Techniques #FOS: Mathematics #FOS: Physical sciences #Hydraulic Fracturing and Reservoir Analysis #Hydrocarbon exploration and reservoir analysis #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.2411.02541

openalex publication_date 2024/11/04 · openalex created_date 2024/11/15 · openalex updated_date 2026/07/28

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.

Cited by

• The odometer in subcritical activated random walk
• Activated random walk on the comb

Related

• The density conjecture for activated random walk
• A new proof of superadditivity and of the density conjecture for Activated Random Walks on the line
• Activated Random Walks on ℤ with Critical Particle Density
• Universality Conjectures for Activated Random Walk
• Random walks in a field of soft traps and criticality for the dissipative Abelian Sandpile Model