Abstract
Abstract
We show that in Abelian sandpiles on infinite Galton–Watson trees, the probability that the total avalanche has more than t topplings decays as $$t^{-1/2}$$t-1/2. We prove both quenched and annealed bounds, under suitable moment conditions. Our proofs are based on an analysis of the conductance martingale of Morris (Probab Theory Relat Fields 125:259–265, 2003), that was previously used by Lyons et al. (Electron J Probab 13(58):1702–1725, 2008) to study uniform spanning forests on $${\mathbb {Z}^d}$$Zd, $$d\ge 3$$d≥3, and other transient graphs.
Publisher
Springer Science and Business Media LLC
Subject
Statistics, Probability and Uncertainty,Statistics and Probability,Analysis