Convergence of the Abelian sandpile

  title={Convergence of the Abelian sandpile},
  author={Wesley Pegden and Charles K. Smart},
  journal={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… 

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