Abstract

One of the most cited physics papers of the 1980s was Bak, Tang and Wiesenfeld’s introduction of self-organized criticality. This theory said that diverse physical systems such as earthquakes, forest fires and avalanches are all governed by similar underlying dynamics and thus they share certain fundamental behaviors. They also proposed a mathematical model that should have all of the properties that define self-organized criticality. Such a model would be called a universal model for self-organized criticality. Abelian networks are a class of models that contain several good candidates for a universal model, including activated random walk and the stochastic sandpile model. We will discuss recent results about these models which give some progress to finding a universal model for self-organized criticality.   This is joint work with Toby Johnson and Matt Junge