Exact sampling and fast mixing of Activated Random Walk
L Levine, F Liang - Electronic Journal of Probability, 2024 - projecteuclid.org
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 …
dimensional lattice Z d. On a finite subset V⊂ Z d it defines a Markov chain on {0, 1} V. We …
Universality and sharpness in activated random walks
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 …
jump distribution and ergodic initial state. We show that the stabilization properties depend …
Separation cutoff for activated random walks
A Bristiel, J Salez - The Annals of Applied Probability, 2024 - projecteuclid.org
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 …
inserted at random and absorbed at the boundary. Despite the nonreversibility of the …
Universality conjectures for activated random walk
L Levine, V Silvestri - Probability Surveys, 2024 - projecteuclid.org
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 …
that the dynamics spontaneously drive the system to a critical state. How universal is this …
Active phase for activated random walks on the lattice in all dimensions
N Forien, A Gaudillière - Annales de l'Institut Henri Poincaré (B) …, 2024 - projecteuclid.org
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 …
than one when the sleep rate λ is small enough, and tends to 0 when λ→ 0, in any …
Macroscopic flow out of a segment for Activated Random Walks in dimension 1
N Forien - arXiv preprint arXiv:2405.04510, 2024 - arxiv.org
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 …
and a conjectured phenomenon of self-organized criticality. In this note, we prove that, in …
On the slow phase for fixed-energy Activated Random Walks
BNB de Limam, LT Rolla, C Terra - arXiv preprint arXiv:2408.07049, 2024 - arxiv.org
We study the Activated Random Walk model on the one-dimensional ring, in the high
density regime. We develop a toppling procedure that gradually builds an environment that …
density regime. We develop a toppling procedure that gradually builds an environment that …
Diffusive bounds for the critical density of activated random walks
A Asselah, LT Rolla, B Schapira - arXiv preprint arXiv:1907.12694, 2019 - arxiv.org
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 …
30 Jul 2019 Page 1 Diffusive bounds for the critical density of activated random walks Amine …
How far do activated random walkers spread from a single source?
L Levine, V Silvestri - Journal of Statistical Physics, 2021 - Springer
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 …
spatial dimension. We prove inner and outer bounds on the spread of n activated random …
Active Phase for Activated Random Walk on
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 …
performs a continuous-time simple symmetric random walk, and falls asleep at rate λ. A …