Exact solutions for a mean-field Abelian sandpile
arXiv:adap-org/9306004 · doi:10.1088/0305-4470/26/19/001
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.
10 pages, LaTeX