Dissipative Abelian sandpiles and random walks.
We show that the dissipative Abelian sandpile on a graph L can be related to a random walk on a graph that consists of L extended with a trapping site. From this relation it can be shown, using exact results and a scaling assumption, that the correlation length exponent nu of the dissipative sandpiles always equals 1/d(w), where d(w) is the fractal dimension of the random walker. This leads to a new understanding of the known result that nu=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.
Vanderzande
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Departement Wiskunde-Natuurkunde-Informatica, Limburgs Universitair Centrum, 3590 Diepenbeek, Belgium.
Daerden
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