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

Author

Listed:
  • Carlson, J. M.
  • Grannan, E. R.
  • Swindle, G. H.

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.

Suggested Citation

  • Carlson, J. M. & Grannan, E. R. & Swindle, G. H., 1993. "A limit theorem for tagged particles in a class of self-organizing particle systems," Stochastic Processes and their Applications, Elsevier, vol. 47(1), pages 1-16, August.
    • Handle: RePEc:eee:spapps:v:47:y:1993:i:1:p:1-16
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