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.
Citation
J. M. Carlson. E. R. Grannan. G. H. Swindle. J. Tour. "Singular Diffusion Limits of a Class of Reversible Self-Organizing Particle Systems." Ann. Probab. 21 (3) 1372 - 1393, July, 1993. https://doi.org/10.1214/aop/1176989122
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