Let G be an infinite graph such that each tree in the wired uniform
spanning forest on G has one end almost surely. On such graphs G, we give a
family of continuous, measure preserving, almost one-to-one mappings from the
wired spanning forest on G to recurrent sandpiles on G, that we call
anchored burning bijections. In the special case of Zd, d≥2,
we show how the anchored bijection, combined with Wilson's stacks of arrows
construction, as well as other known results on spanning trees, yields a power
law upper bound on the rate of convergence to the sandpile measure along any
exhaustion of Zd. We discuss some open problems related to these
findings.Comment: 26 pages; 1 EPS figure. Minor alterations made after comments from
refere