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

Antal Jarai; W.M. Ruszel; Ellen Saada

doi:10.1007/s00440-019-00951-z

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

Antal Jarai
, W.M. Ruszel
, Ellen Saada

Research output: Contribution to journal › Article › Academic › peer-review

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.

Original language	English
Pages (from-to)	369-396
Journal	Probability Theory and Related Fields
Volume	177
DOIs	https://doi.org/10.1007/s00440-019-00951-z
Publication status	Published - Jun 2020
Externally published	Yes

Keywords

Abelian sandpile
Uniform spanning tree
Conductance martingale
Wired spanning forest

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2020_Article_Final published version, 441 KBLicence: CC BY

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title = "Mean-field avalanche size exponent for sandpiles on Galton-Watson trees",

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.",

keywords = "Abelian sandpile, Uniform spanning tree, Conductance martingale, Wired spanning forest",

author = "Antal Jarai and W.M. Ruszel and Ellen Saada",

year = "2020",

month = jun,

doi = "10.1007/s00440-019-00951-z",

language = "English",

volume = "177",

pages = "369--396",

journal = "Probability Theory and Related Fields",

issn = "0178-8051",

publisher = "Springer New York",

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TY - JOUR

T1 - Mean-field avalanche size exponent for sandpiles on Galton-Watson trees

AU - Jarai, Antal

AU - Ruszel, W.M.

AU - Saada, Ellen

PY - 2020/6

Y1 - 2020/6

N2 - 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.

AB - 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.

KW - Abelian sandpile

KW - Uniform spanning tree

KW - Conductance martingale

KW - Wired spanning forest

U2 - 10.1007/s00440-019-00951-z

DO - 10.1007/s00440-019-00951-z

M3 - Article

SN - 0178-8051

VL - 177

SP - 369

EP - 396

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

ER -

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

Abstract

Keywords

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