Thu, January 15, 2026
10:20 am - 11:15 am
Math Tower (MW) 154
Josh Meisel
City University of New York (CUNY)
Title
Self-organized criticality in biased Activated Random Walk
Abstract
Activated Random Walk (ARW) is a sandpile model intended to robustly—and provably—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 proves many SOC and other conjectures. For the first time in any setting we prove the existence of a critical state, shared by both the canonical model at its critical value, as well as several variants with no tunable parameter. We also establish non-fixation at criticality, and show avalanches are finite with critical exponent at most 1/2.