7 papers
Stationary activated random walk: regularity, heavy tails, and remixing
Tobias Johnson, Matthew Junge, Josh Meisel
We study the stationary state of driven-dissipative activated random walk on an interval of length and prove that subintervals down to size have particle density near…
Activated random walk exhibits self-organized criticality
Christopher Hoffman, Tobias Johnson, Matthew Junge +1
To explain the ubiquity of power laws and fractals in nature, Bak, Tang, and Wiesenfeld formulated simple conditions for a system to self-organize into a critical state. Dickman, M…
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 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.…
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…