Exact solutions for a mean-field Abelian sandpile
Steven A. Janowsky, Claude A. Laberge
Abstract
We introduce a model for a sandpile, with N sites, critical height N and each site connected to every other site. It is thus a mean-field model in the spin-glass sense. We find an exact solution for the steady state probability distribution of avalanche sizes, and discuss its asymptotics for large N.
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