Activated Random Walks, on Z d for any d≥ 1, is an interacting particle system, where
particles can be in either of two states: active or frozen. Each active particle performs a …

Abstract Activated Random Walk (ARW) is an interacting particle system on the d-
dimensional lattice Z d. On a finite subset V⊂ Z d it defines a Markov chain on {0, 1} V. We …

We consider activated random walks on arbitrary finite networks, with particles being
inserted at random and absorbed at the boundary. Despite the nonreversibility of the …

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 …

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 …

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 …

Unlike many particle systems, activated random walk has nontrivial behavior even in one
spatial dimension. We prove inner and outer bounds on the spread of n activated random …

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 …

In ballistic annihilation, infinitely many particles with randomly assigned velocities move
across the real line and mutually annihilate upon contact. We introduce a variant with …

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 …