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

• 成果类型: Article
• 署名作者: Jarai, Antal A.; Ruszel, Wioletta M.; Saada, Ellen
• 署名单位: University of Bath; Delft University of Technology; Utrecht University; Universite Paris Cite; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-019-00951-z
• 发表日期: 2020
• 页码: 369-396
• 关键词: infinite volume limit; MODEL

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.