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Asymptotics for 2D critical and near-critical first-passage percolation
Yao, Chang-Long
2019-12-01
Source PublicationPROBABILITY THEORY AND RELATED FIELDS
ISSN0178-8051
Volume175Issue:3-4Pages:975-1019
AbstractWe 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.
KeywordPercolation First passage percolation Correlation length Scaling limit Conformal loop ensemble
DOI10.1007/s00440-019-00908-2
Indexed BySCI
Language英语
Funding ProjectNational Natural Science Foundation of China[11601505] ; NSFC[11688101] ; Key Laboratory of Random Complex Structures and Data Science, CAS[2008DP173182]
WOS Research AreaMathematics
WOS SubjectStatistics & Probability
WOS IDWOS:000493683800010
PublisherSPRINGER HEIDELBERG
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/50631
Collection中国科学院数学与系统科学研究院
Corresponding AuthorYao, Chang-Long
AffiliationChinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China
Recommended Citation
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.
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