The Density Conjecture for Activated Random Walk

Explore the concept of self-organized criticality in physical systems through this lecture on the density conjecture for activated random walk. Delve into the mathematical modeling of phenomena like earthquakes and avalanches, where energy accumulates slowly and releases suddenly. Examine the key feature of fat-tailed energy release distributions and their polynomial decay. Investigate the activated random walk model as a promising approach to demonstrating self-organized criticality in statistical physics. Learn about various starting configurations for activated random walk on lines and cycles, and discover how they all share a common critical density. Gain insights from the joint work of Christopher Hoffman, Toby Johnson, and Matthew Junge, presented at IPAM's Statistical Mechanics Beyond 2D Workshop.