Abstract
We analyze the abelian sandpile model on ℤd 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 (J. Stat. Phys. 198:143–159, 2010) that the radius of the toppled cluster of this configuration is O(n 1/d).
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Acknowledgements
I would like to thank Béla Bollobás and Rob Morris for drawing this problem to my attention and for their help and advice. My thanks to the anonymous reviewers for their helpful remarks.
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Tyomkyn, M. A Note on the Abelian Sandpile in \(\pmb{\mathbb{Z}}^{d}\) . J Stat Phys 148, 1072–1075 (2012). https://doi.org/10.1007/s10955-012-0564-0
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DOI: https://doi.org/10.1007/s10955-012-0564-0