# Convergence of the Abelian sandpile

@article{Pegden2011ConvergenceOT,
title={Convergence of the Abelian sandpile},
author={Wesley Pegden and Charles K. Smart},
journal={Duke Mathematical Journal},
year={2011},
volume={162},
pages={627-642}
}
• Published 30 April 2011
• Mathematics
• Duke Mathematical Journal
The Abelian sandpile growth model is a diffusion process for configurations of chips placed on vertices of the integer lattice $\mathbb{Z}^d$, in which sites with at least 2d chips {\em topple}, distributing 1 chip to each of their neighbors in the lattice, until no more topplings are possible. From an initial configuration consisting of $n$ chips placed at a single vertex, the rescaled stable configuration seems to converge to a particular fractal pattern as $n\to \infty$. However, little has…
43 Citations

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