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
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Journal of Statistical Physics

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