Asymptotic height distribution in high-dimensional sandpiles

Abstract

We give an asymptotic formula for the single site height distribution of Abelian sandpiles on ${\mathbb{Z}}^d$ as $d\to \infty$, in terms of $\mathsf{Poisson}(1)$ probabilities. We provide error estimates.

12 pages

References in corpus (1)

• Anchored burning bijections on finite and infinite graphs