Singular Diffusion Limits of a Class of Reversible Self-Organizing Particle Systems

Abstract

We establish hydrodynamic limits for a class of attractive, reversible particle systems with an infinite range of interaction. The limiting nonlinear diffusion equations have diffusion coefficients which are functions of the local density, and which have a singularity at a critical value of the density. On open driven systems, these singular diffusion limits explain the observed nontrivial scaling behavior known as self-organized criticality.