5 papers · 1 filter
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.…
Explosivity in 1-d Activated Random Walk
Nicolas Forien, Christopher Hoffman, Tobias Johnson +3
We show that Activated Random Walk on is explosive above criticality. That is, activating a single particle in a supercritical state of sleeping particles triggers an…
The odometer in subcritical activated random walk
Tobias Johnson, Jacob Richey
We consider the activated random walk particle system, a model of self-organized criticality, on with i.i.d.-Bernoulli initial configuration. We show that at subcritic…
Cutoff for activated random walk
Christopher Hoffman, Tobias Johnson, Matthew Junge +1
We prove that the mixing time of driven-dissipative activated random walk on an interval of length with uniform or central driving exhibits cutoff at times the critical den…
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…