Self-organized criticality in biased Activated Random Walk

Abstract: Activated Random Walk (ARW) is a sandpile model intended to robustly exhibit self-organized criticality (SOC), a proposed explanation from physics for how natural systems display critical behavior without any external tuning to a phase transition. I will discuss an upcoming work on asymmetric one-dimensional ARW which verifies many predictions for the model. Namely, the existence of a critical state is established, shared by both the canonical model at its critical value, as well as several variants with no tunable parameter. At criticality, it is shown that the system does not fixate, and avalanches are finite with critical exponent at most 1/2.