  We prove that Abelian sandpiles with random initial states converge almost
surely to unique scaling limits. The proof follows the Armstrong-Smart program
for stochastic homogenization of uniformly elliptic equations.
  Using simple random walk estimates, we prove an analogous result for the
divisible sandpile and identify its scaling limit as exactly that of the
averaged divisible sandpile. As a corollary, this gives a new quantitative
proof of known results on the stabilizability of Abelian sandpiles.
