The odometer in subcritical activated random walk

2025/10/07 by Johnson, Tobias, Richey, Jacob
#60K35 #82C22 #FOS: Mathematics #FOS: Physical sciences #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2510.05514

Abstract

We consider the activated random walk particle system, a model of self-organized criticality, on ℤ with i.i.d.-Bernoulli initial configuration. We show that at subcritical density, the system's odometer function, which counts the number of actions taken at each site, has a stretched exponential tail. It follows that the expected odometer at each site is finite.

Citations

• Mean-field limit for activated random walk on the integer lattice
• A new proof of superadditivity and of the density conjecture for Activated Random Walks on the line
• Cutoff for activated random walk
• The hockey-stick conjecture for activated random walk
• The density conjecture for activated random walk
• Universality Conjectures for Activated Random Walk
• Critical density of activated random walks on transitive graphs
• Non-fixation for conservative stochastic dynamics on the line
• Absorbing-state transition for Stochastic Sandpiles and Activated Random\n Walks
• Oil and water: a two-type internal aggregation model
• The Apollonian structure of integer superharmonic matrices
• Apollonian structure in the Abelian sandpile

Related

• Activated Random Walks on ℤ with Critical Particle Density
• The density conjecture for activated random walk
• The hockey-stick conjecture for activated random walk
• The number of particles in activated random walk on the complete graph
• A new proof of superadditivity and of the density conjecture for Activated Random Walks on the line