Asymptotics for 2D critical and near-critical first-passage percolation

doi:10.1007/s00440-019-00908-2

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	Asymptotics for 2D critical and near-critical first-passage percolation
	Yao, Chang-Long
	2019-12-01
发表期刊	PROBABILITY THEORY AND RELATED FIELDS
ISSN	0178-8051
卷号	175 期号:3-4 页码:975-1019
摘要	We study Bernoulli first-passage percolation (FPP) on the triangular lattice in which sites have 0 and 1 passage times with probability p and 1- p, respectively. Denote by C8 the infinite cluster with 0-time sites when p > pc, where pc = 1/2 is the critical probability. Denote by T (0, C8) the passage time from the origin 0 to C8. First we obtain explicit limit theorem for T (0, C8) as p pc. The proof relies on the limit theorem in the critical case, the critical exponent for correlation length and Kesten's scaling relations. Next, for the usual point-to-point passage time a0, n in the critical case, we construct subsequences of sites with different growth rate along the axis. The main tool involves the large deviation estimates on the nesting of CLE6 loops derived by Miller et al. (Ann Probab 44:1013-1052, 2016). Finally, we apply the limit theorem for critical Bernoulli FPP to a random graph called cluster graph, obtaining explicit strong law of large numbers for graph distance.
关键词	Percolation First passage percolation Correlation length Scaling limit Conformal loop ensemble
DOI	10.1007/s00440-019-00908-2
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[11601505] ; NSFC[11688101] ; Key Laboratory of Random Complex Structures and Data Science, CAS[2008DP173182]
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000493683800010
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/50631
专题	应用数学研究所
通讯作者	Yao, Chang-Long
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Yao, Chang-Long. Asymptotics for 2D critical and near-critical first-passage percolation[J]. PROBABILITY THEORY AND RELATED FIELDS,2019,175(3-4):975-1019.
APA	Yao, Chang-Long.(2019).Asymptotics for 2D critical and near-critical first-passage percolation.PROBABILITY THEORY AND RELATED FIELDS,175(3-4),975-1019.
MLA	Yao, Chang-Long."Asymptotics for 2D critical and near-critical first-passage percolation".PROBABILITY THEORY AND RELATED FIELDS 175.3-4(2019):975-1019.