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arXiv · 1102.4470

A note on the abelian sandpile in Z^d

Mykhaylo Tyomkyn
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Abstract

We analyse the abelian sandpile model on $\mathbbm{Z}^d$ for the starting configuration of $n$ particles in the origin and $2d-2$ particles otherwise. We give a new short proof of the theorem of Fey, Levine and Peres \cite{FLP} that the radius of the toppled cluster of this configuration is $O(n^{1/d})$.

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Mykhaylo Tyomkyn. 2011-02-22. A note on the abelian sandpile in Z^d. https://doi.org/10.1007/s10955-012-0564-0

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