The hockey-stick conjecture for activated random walk

Christopher Hoffman; Tobias Johnson; Matthew Junge

doi:10.1090/proc/17656

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arXiv · 2411.02541

The hockey-stick conjecture for activated random walk

Christopher Hoffman·Tobias Johnson·Matthew Junge

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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.

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Christopher Hoffman, Tobias Johnson, Matthew Junge. 2024-11-04. The hockey-stick conjecture for activated random walk. https://doi.org/10.1090/proc/17656

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