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.
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页码：369 / 396
页数：28
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