We study the abelian sandpile growth model, where n particles are added at the origin on a stable background configuration in Z^d. Any site with at least 2d particles then topples by sending one particle to each neighbor. We find that with constant background height h <= 2d-2, the diameter of the set of sites that topple has order n^{1/d}. This was previously known only for h
abelian sandpile, bootstrap percolation, dimensional reduction, discrete Laplacian, growth model, least action principle
Interacting random processes; statistical mechanics type models; percolation theory (msc 60K35)
Logistics (theme 3), Energy (theme 4)
Springer
Journal of Statistical Physics
Stochastics

Fey, A.C, Levine, L, & Peres, Y. (2010). Growth rates and explosions in sandpiles. Journal of Statistical Physics, 138, 143–159.