Lionel Levine, Vittoria Silvestri
Probab. Surveys 21, 1-27, (2024) DOI: 10.1214/24-PS25
KEYWORDS: Abelian network, Activated random walk, hyperuniformity, incompressibility, microscopic limit, quadrature inequality, Scaling limit, spatial mixing, stationary distribution, temporal mixing, 60K35, 82C22, 82C26, 82B26, 82B27
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 critical state? We state many interlocking conjectures aimed at different aspects of this question: scaling limits, microscopic limits, temporal and spatial mixing, incompressibility, and hyperuniformity.
