A LIMIT-THEOREM FOR TAGGED PARTICLES IN A CLASS OF SELF-ORGANIZING PARTICLE-SYSTEMS

The dynamics of tagged particles in a class of models which can exhibi t nontrivial scaling behavior (self-organized criticality (SOC)) is in vestigated. Previously it was shown that in the hydrodynamic limit the se 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. W e establish a functional central limit theorem for the rescaled positi on of a tagged particle in each model, and we establish asymptotics fo r the variance of the limiting Brownian motion as the density approach es unit (critical) density. We expect these methods will provide a use ful means of characterizing the dynamics in related self-organizing sy stems.