Growth Rates and Explosions in Sandpiles

Understand

We study the abelian sandpile growth model, where n particles are added at the origin on a stable background configuration in Z^d.

• Any site with at least 2d particles then topples by sending one particle to each neighbor.
• We find that with constant background height h <= 2d-2, the diameter of the set of sites that topple has order n^{1/d}.
• This was previously known only for h<d.