We consider the activated random walk model in any dimension with any sleep rate and
jump distribution and ergodic initial state. We show that the stabilization properties depend …

Abstract Activated Random Walk is a particle system displaying Self-Organized Criticality, in
that the dynamics spontaneously drive the system to a critical state. How universal is this …

We show that the critical density of the Activated Random Walk model on Z d is strictly less
than one when the sleep rate λ is small enough, and tends to 0 when λ→ 0, in any …

Abstract We consider Activated Random Walk (ARW), a particle system with mass
conservation, on the cycle Z/nZ. One starts with a mass density μ>0 of initially active …

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, in …

It has been conjectured that the critical density of the Activated Random Walk model is
strictly less than one for any value of the sleeping rate. We prove this conjecture on Z^d …

Diffusive bounds for the critical density of activated random walks arXiv:1907.12694v1 [math.PR]
30 Jul 2019 Page 1 Diffusive bounds for the critical density of activated random walks Amine …

Abstract We consider the Activated Random Walk model on Z. In this model, each particle
performs a continuous-time simple symmetric random walk, and falls asleep at rate λ. A …

Some stochastic systems are particularly interesting as they exhibit critical behavior without
fine-tuning of a parameter, a phenomenon called self-organized criticality. In the context of …

We prove that in wide generality the critical curve of the activated random walk model is a
continuous function of the deactivation rate, and we provide a bound on its slope, which is …