3 citations · 7 across the 12 of their papers we have counts for
12 papers · 1 filter
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…
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…
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…
Coexistence, enhancements and short loops in random walk loop soups
Nicolas Forien, Matteo Quattropani, Alexandra Quitmann +1
We consider a general random walk loop soup which includes, or is related to, several models of interest, such as the Spin O(N) model, the double dimer model and the Bose gas. The…
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…
Active Phase for Activated Random Walks on the Lattice in all Dimensions
Nicolas Forien, Alexandre Gaudillière
We show that the critical density of the Activated Random Walk model on is strictly less than one when the sleep rate is small enough, and tends to when $λ\t…
An extension of the Ising-Curie-Weiss model of self-organized criticality with a threshold on the interaction range
Nicolas Forien
In arXiv:1301.6911, Cerf and Gorny constructed a model of self-organized criticality, by introducing an automatic control of the temperature parameter in the generalized Ising Curi…
An extension of the Ising-Curie-Weiss model of self-organized criticality with long range interactions
Nicolas Forien
In [CG16], Cerf and Gorny constructed a model of self-organized criticality, by introducing an automatic control of the temperature parameter in the generalized Ising Curie-Weiss m…
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…
Some toy models of self-organized criticality in percolation
Raphaël Cerf, Nicolas Forien
We consider the Bernoulli percolation model in a finite box and we introduce an automatic control of the percolation probability, which is a function of the percolation configurati…