KMS Of Academy of mathematics and systems sciences, CAS
Asymptotics for 2D critical and near-critical first-passage percolation | |
Yao, Chang-Long | |
2019-12-01 | |
Source Publication | PROBABILITY THEORY AND RELATED FIELDS |
ISSN | 0178-8051 |
Volume | 175Issue:3-4Pages:975-1019 |
Abstract | 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. |
Keyword | Percolation First passage percolation Correlation length Scaling limit Conformal loop ensemble |
DOI | 10.1007/s00440-019-00908-2 |
Indexed By | SCI |
Language | 英语 |
Funding Project | National Natural Science Foundation of China[11601505] ; NSFC[11688101] ; Key Laboratory of Random Complex Structures and Data Science, CAS[2008DP173182] |
WOS Research Area | Mathematics |
WOS Subject | Statistics & Probability |
WOS ID | WOS:000493683800010 |
Publisher | SPRINGER HEIDELBERG |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/50631 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | Yao, Chang-Long |
Affiliation | Chinese 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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