We study the stationary distribution of the standard Abelian sandpile model in the box Λ n=[-
n, n] d∩ ℤ d for d≥ 2. We show that as n→∞, the finite volume stationary distributions
weakly converge to a translation invariant measure on allowed sandpile configurations in ℤ
d. This allows us to define infinite volume versions of the avalanche-size distribution and
related quantities. The proof is based on a mapping of the sandpile model to the uniform
spanning tree due to Majumdar and Dhar, and the existence of the wired uniform spanning …

We study the stationary distribution of the standard Abelian sandpile model in the box $
Lam_n=[-n, n]^ d cap d $ for $ d ge 2$. We show that as $ no infty $, the finite volume
stationary distributions weakly converge to a translation invariant measure on allowed
sandpile configurations in $ d $. This allows us to define infinite volume versions of the
avalanche-size distribution and related quantities. The proof is based on a mapping of the
sandpile model to the uniform spanning tree due to Majumdar and Dhar, and the existence …