Growth Rates and Explosions in Sandpiles

@article{Fey2009GrowthRA,
  title={Growth Rates and Explosions in Sandpiles},
  author={Anne Fey and Lionel Levine and Yuval Peres},
  journal={Journal of Statistical Physics},
  year={2009},
  volume={138},
  pages={143-159}
}
We study the abelian sandpile growth model, where n particles are added at the origin on a stable background configuration in ℤd. 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 n1/d. This was previously known only for h<d. Our proof uses a strong form of the least action principle for sandpiles, and a novel method of background modification.We… 
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