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Dissipative Abelian Sandpiles and Random Walks

C. Vanderzande·F. Daerden
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Abstract

We show that the dissipative Abelian sandpile on a graph L can be related to a random walk on a graph which consists of L extended with a trapping site. From this relation it can be shown, using exact results and a scaling assumption, that the dissipative sandpiles' correlation length exponent νalways equals 1/d_w, where d_w is the fractal dimension of the random walker. This leads to a new understanding of the known results that ν=1/2 on any Euclidean lattice. Our result is however more general and as an example we also present exact data for finite Sierpinski gaskets which fully confirm our predictions.

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C. Vanderzande, F. Daerden. 2001-01-03. Dissipative Abelian Sandpiles and Random Walks. https://doi.org/10.1103/physreve.63.030301

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