  We consider a continuous height version of the Abelian sandpile model with
small amount of bulk dissipation gamma > 0 on each toppling, in dimensions d =
2, 3. In the limit gamma -> 0, we give a power law upper bound, based on
coupling, on the rate at which the stationary measure converges to the discrete
critical sandpile measure. The proofs are based on a coding of the stationary
measure by weighted spanning trees, and an analysis of the latter via Wilson's
algorithm. In the course of the proof, we prove an estimate on coupling a
geometrically killed loop-erased random walk to an unkilled loop-erased random
walk.
