Growth Rates and Explosions in Sandpiles

Details Growth Rates and Explosions in Sandpiles Growth Rates and Explosions in Sandpiles

2009-01-24

arxiv.org/abs/0901.3805v2

J. Stat. Phys. 138, 143--159 (2010)

Mathematics

Combinatorics

19 pages, 4 figures, to appear in Journal of Statistical Physics. v2 corrects the proof of the outer bound of Theorem 4.1 of a

Scientific paper

10.1007/s10955-009-9899-6

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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