A limit theorem for tagged particles in a class of self-organizing particle systems

AbstractThe dynamics of tagged particles in a class of models which can exhibit nontrivial scaling behavior (self-organized criticality (SOC) is investigated. Previously it was shown that in the hydrodynamic limit these models are described by diffusion equations with singular diffusion coefficients—a fact which explains the self-organizing behavior. Here we develop an alternate means for identifying SOC in these systems. We establish a functional central limit theorem for the rescaled position of a tagged particle in each model, and we establish asymptotics for the variance of the limiting Brownian motion as the density approaches unit (critical) density. We expect these methods will provide a useful means of characterizing the dynamics in related self-organizing systems