The Abelian Sandpile model on an infinite tree

• 成果类型: Article
• 署名作者: Maes, C; Redig, F; Saada, E
• 署名单位: KU Leuven; Eindhoven University of Technology; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2002
• 页码: 2081-2107
• 关键词: self-organized criticality

摘要

We consider the standard Abelian sandpile process on the Bethe lattice. We show the existence of the thermodynamic limit for the finite volume stationary measures and the existence of a unique infinite volume Markov process exhibiting features of self-organized criticality.