Dissipative sandpile models with universal exponents

We consider a dissipative variant of the stochastic-Abelian sandpile model on a two-dimensional lattice. The boundaries are closed and the dissipation is due to the fact that each toppled grain is removed from the lattice with probability. It is shown that the scaling properties of this model are in the universality class of the stochastic-Abelian models with conservative dynamics and open boundaries. In particular, the dissipation rate can be adjusted according to a suitable function =f(L), such that the avalanche size distribution will coincide with that of the conservative model on a finite lattice of size L.