CSpace  > 应用数学研究所
Limit theorems for critical first-passage percolation on the triangular lattice
Yao, Chang-Long
2018-02-01
Source PublicationSTOCHASTIC PROCESSES AND THEIR APPLICATIONS
ISSN0304-4149
Volume128Issue:2Pages:445-460
AbstractConsider (independent) first-passage percolation on the sites of the triangular lattice T embedded in C. Denote the passage time of the site v in T by t(v), and assume that P(t(v) = 0) = P(t(v) = 1) = 1/2. Denote by b(0,n) the passage time from 0 to the halfplane {v is an element of T : Re(v) >= n}, and by T(0, nu) the passage time from 0 to the nearest site to nu, where vertical bar u vertical bar = 1. We prove that as n -> infinity, b(0,n)/ log n -> 1/(2 root 3 pi) a.s., E[b(0,n)]/ log n -> 1/(2 root 3 pi) and Var[b(0,n)]/ log -> n 2/(3 root 3 pi) - 1/(2 pi(2)); T(0, nu)/ log n -> 1/(root 3 pi) in probability but not a.s., E[T (0, nu)]/ log n -> 1/(root 3 pi) and Var[T(0, nu)]/ log n -> 4/(3 root 3 pi) - 1/pi(2). This answers a question of Kesten and Zhang (1997) and improves our previous work (2014). From this result, we derive an explicit form of the central limit theorem for b(0,n) and T (0, nu). A key ingredient for the proof is the moment generating function of the conformal radii for conformal loop ensemble CLE6, given by Schramm et al. (2009). (C) 2017 Elsevier B.V. All rights reserved.
KeywordCritical percolation First-passage percolation Scaling limit Conformal loop ensemble Law of large numbers Central limit theorem
DOI10.1016/j.spa.2017.05.002
Language英语
Funding ProjectNational Natural Science Foundation of China[11601505] ; Key Laboratory of Random Complex Structures and Data Science, CAS[2008DP173182]
WOS Research AreaMathematics
WOS SubjectStatistics & Probability
WOS IDWOS:000423887100004
PublisherELSEVIER SCIENCE BV
Citation statistics
Cited Times:1[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29470
Collection应用数学研究所
AffiliationChinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Yao, Chang-Long. Limit theorems for critical first-passage percolation on the triangular lattice[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS,2018,128(2):445-460.
APA Yao, Chang-Long.(2018).Limit theorems for critical first-passage percolation on the triangular lattice.STOCHASTIC PROCESSES AND THEIR APPLICATIONS,128(2),445-460.
MLA Yao, Chang-Long."Limit theorems for critical first-passage percolation on the triangular lattice".STOCHASTIC PROCESSES AND THEIR APPLICATIONS 128.2(2018):445-460.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Bookmark
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Yao, Chang-Long]'s Articles
Baidu academic
Similar articles in Baidu academic
[Yao, Chang-Long]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Yao, Chang-Long]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.
 

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.