A Note on the Abelian Sandpile in ℤ d

Mykhaylo Tyomkyn

doi:10.1007/s10955-012-0564-0

A Note on the Abelian Sandpile in ℤ ^d

Mykhaylo Tyomkyn^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We analyze the abelian sandpile model on 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 (J. Stat. Phys. 198:143-159, 2010) that the radius of the toppled cluster of this configuration is O(n ^1/d).

Original language	English
Pages (from-to)	1072-1075
Number of pages	4
Journal	Journal of Statistical Physics
Volume	148
Issue number	6
DOIs	https://doi.org/10.1007/s10955-012-0564-0
State	Published - Sep 2012
Externally published	Yes

Keywords

Abelian sandpile model
Cellular automata
Self-organized criticality

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10.1007/s10955-012-0564-0

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abstract = "We analyze the abelian sandpile model on 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 (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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KW - Cellular automata

KW - Self-organized criticality

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A Note on the Abelian Sandpile in ℤ ^d

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Keywords

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