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

Antal Jarai, Wioletta Magdalena Ruszel, Ellen Saada

Research output: Contribution to journalArticle

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

Original languageEnglish
Pages (from-to)369-396
Number of pages28
JournalProbability Theory and Related Fields
Volume177
Early online date3 Nov 2019
DOIs
Publication statusPublished - 1 Jun 2020

Keywords

  • Abelian sandpile
  • uniform spanning tree
  • conductance martingale
  • Wired spanning forest
  • Conductance martingale
  • Uniform spanning tree

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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