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

Title

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

 Author

Jarai, Antal A. (University of Bath)
Ruszel, W.M. (TU Delft Applied Probability; Universiteit Utrecht)
Saada, Ellen (Université Paris Descartes)

Date

2019

 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.


 Subject

Abelian sandpile
Conductance martingale
Uniform spanning tree
Wired spanning forest

 To reference this document use:

http://resolver.tudelft.nl/uuid:71577764-537d-48d2-91ad-e8e792cf7801

 DOI

https://doi.org/10.1007/s00440-019-00951-z

 ISSN

0178-8051

 Source

Probability Theory and Related Fields, 177 (2020) (1-2), 369-396

 Part of collection

Institutional Repository

 Document type

journal article

 Rights

© 2019 Antal A. Jarai, W.M. Ruszel, Ellen Saada
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