3 papers
math.PR2026
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…
math.PR2025
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…
math.PR2025
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…