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math.PR2024
The hockey-stick conjecture for activated random walk
Christopher Hoffman, Tobias Johnson, Matthew Junge
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.…
math.PR2024
The density conjecture for activated random walk
Christopher Hoffman, Tobias Johnson, Matthew Junge
Bak, Tang, and Wiesenfeld developed their theory of self-organized criticality in the late 1980s to explain why many real-life processes exhibit signs of critical behavior despite…