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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
A new proof of superadditivity and of the density conjecture for Activated Random Walks on the line
Nicolas Forien
In two recent works, Hoffman, Johnson and Junge proved the density conjecture, the hockey stick conjecture and the ball conjecture for Activated Random Walks in dimension one, show…
math.PR2020
A planar Ising model of self-organized criticality
Nicolas Forien
We consider the planar Ising model in a finite square box and we replace the temperature parameter with a function depending on the magnetization. This creates a feedback from the…