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

文献类型：期刊论文

作者Yao, Chang-Long
刊名PROBABILITY THEORY AND RELATED FIELDS
出版日期2019-12-01
卷号175期号:3-4页码:975-1019
关键词Percolation First passage percolation Correlation length Scaling limit Conformal loop ensemble
ISSN号0178-8051
DOI10.1007/s00440-019-00908-2
英文摘要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.
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
语种英语
WOS记录号WOS:000493683800010
出版者SPRINGER HEIDELBERG
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/50630]  
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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