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

被引：1

作者：

Jarai, Antal A. ^{[1
]}

Ruszel, Wioletta M. ^{[2
,3
]}

Saada, Ellen ^{[4
]}

机构：

[1] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England

[2] Delft Univ Technol, Delft Inst Appl Math, Van Mourik Broekmanweg 6, NL-2628 XE Delft, Netherlands

[3] Univ Utrecht, Math Inst, Budapestlaan 6, NL-3584 CD Utrecht, Netherlands

[4] Univ Paris 05, Lab MAP5, CNRS, UMR 8145, 45 Rue St Peres, F-75270 Paris 06, France

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2020年 / 177卷 / 1-2期

关键词：

Abelian sandpile; Uniform spanning tree; Conductance martingale; Wired spanning forest; INFINITE VOLUME LIMIT; MODEL;

D O I：

10.1007/s00440-019-00951-z

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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), thatwas 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.

引用

页码：369 / 396

页数：28

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