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. 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 Z d, d≥ 3 , and other transient graphs.
- Abelian sandpile
- uniform spanning tree
- conductance martingale
- Wired spanning forest
- Conductance martingale
- Uniform spanning tree
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
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- Department of Mathematical Sciences - Senior Lecturer
- EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
- Probability Laboratory at Bath
Person: Research & Teaching