Dissipative Abelian sandpiles and random walks - art. no. 030301

We show that the dissipative Abelian sandpile on a graph L can be related t o 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 ass umption, that the correlation length exponent nu of the dissipative sandpil es always equals 1/d(w) where d(w) is the fractal dimension of the random w alker. This leads to a new understanding of the known result that v = 1/2 o n any Euclidean lattice. Our result is, however, more general, and as an ex ample we also present exact data for finite Sierpinski gaskets, which fully confirm our predictions.