7 papers · 1 filter
Stochastic Sandpile Model: exact sampling and complete graph
Concetta Campailla, Nicolas Forien
We study the dynamics of the Stochastic Sandpile Model on finite graphs, with two main results. First, we describe a procedure to exactly sample from the stationary distribution of…
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…
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…
The critical density of the Stochastic Sandpile Model
Concetta Campailla, Nicolas Forien, Lorenzo Taggi
We study the stochastic sandpile model on and demonstrate that the critical density is strictly less than one in all dimensions. This generalizes a previous result b…
Macroscopic flow out of a segment for Activated Random Walks in dimension 1
Nicolas Forien
Activated Random Walk is a system of interacting particles which presents a phase transition and a conjectured phenomenon of self-organized criticality. In this note, we prove that…
The Critical Density for Activated Random Walks is always less than 1
Amine Asselah, Nicolas Forien, Alexandre Gaudillière
Activated Random Walks, on for any , is an interacting particle system, where particles can be in either of two states: active or frozen. Each active p…