Height probabilities in the Abelian sandpile model on the generalized finite Bethe lattice

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	Height probabilities in the Abelian sandpile model on the generalized finite Bethe lattice
	Chen, Haiyan ; Zhang, Fuji ; Zhang FJ(张福基)
刊名	http://dx.doi.org/10.1063/1.4817089
	2013
关键词	SELF-ORGANIZED CRITICALITY GRAPHS
英文摘要	National Natural Science Foundation of China [NSFC11171134]; Natural Science Foundation of Fujian Province, China [2011J01015]; In this paper, we study the sandpile model on the generalized finite Bethe lattice with a particular boundary condition. Using a combinatorial method, we give the exact expressions for all single-site probabilities and some two-site joint probabilities. As a by-product, we prove that the height probabilities of bulk vertices are all the same for the Bethe lattice with certain given boundary condition, which was found from numerical evidence by Grassberger and Manna ["Some more sandpiles," J. Phys. (France) 51, 1077-1098 (1990)] but without a proof. (C) 2013 AIP Publishing LLC.
语种	英语
出版者	AMER INST PHYSICS
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/91257]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Chen, Haiyan,Zhang, Fuji,Zhang FJ. Height probabilities in the Abelian sandpile model on the generalized finite Bethe lattice[J]. http://dx.doi.org/10.1063/1.4817089,2013.
APA	Chen, Haiyan,Zhang, Fuji,&张福基.(2013).Height probabilities in the Abelian sandpile model on the generalized finite Bethe lattice.http://dx.doi.org/10.1063/1.4817089.
MLA	Chen, Haiyan,et al."Height probabilities in the Abelian sandpile model on the generalized finite Bethe lattice".http://dx.doi.org/10.1063/1.4817089 (2013).