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.