Growth rates and explosions in sandpiles

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

Additional Metadata
Keywords	abelian sandpile, bootstrap percolation, dimensional reduction, discrete Laplacian, growth model, least action principle
MSC	Interacting random processes; statistical mechanics type models; percolation theory (msc 60K35)
THEME	Logistics (theme 3), Energy (theme 4)
Publisher	Springer
Journal	Journal of Statistical Physics
Organisation	Stochastics
Citation APA Style AAA Style APA Style Cell Style Chicago Style Harvard Style IEEE Style MLA Style Nature Style Vancouver Style American-Institute-of-Physics Style Council-of-Science-Editors Style BibTex Format Endnote Format RIS Format CSL Format DOIs only Format	Fey, A., Levine, L., & Peres, Y. (2010). Growth rates and explosions in sandpiles. Journal of Statistical Physics, 138, 143–159.