Mean-field avalanche size exponent for sandpiles on Galton–Watson trees

Journal article (2019)

Authors

Antal A. Jarai University of Bath
W.M. Ruszel Universiteit Utrecht, Applied Probability - EEMCS
Ellen Saada Université Paris Descartes
Research Group
Applied Probability (EEMCS) (TU Delft)
Copyright: © 2019 Antal A. Jarai, W.M. Ruszel, Ellen Saada
DOI: https://doi.org/10.1007/s00440-019-00951-z
More Info
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Published Date

2019

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Applied Probability

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. 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 Zd, d≥ 3 , and other transient graphs.