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

J. M. Carlson, E. R. Grannan and G. H. Swindle

Stochastic Processes and their Applications, 1993, vol. 47, issue 1, 1-16

Abstract: The 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.

Keywords: tagged; particles; self-organized; criticality; functional; central; limit; theorem (search for similar items in EconPapers)
Date: 1993
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