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 Publication STOCHASTIC PROCESSES AND THEIR APPLICATIONS ISSN 0304-4149 Volume 128Issue:2Pages:445-460 Abstract Consider (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. Keyword Critical percolation First-passage percolation Scaling limit Conformal loop ensemble Law of large numbers Central limit theorem DOI 10.1016/j.spa.2017.05.002 Language 英语 Funding Project National Natural Science Foundation of China[11601505] ; Key Laboratory of Random Complex Structures and Data Science, CAS[2008DP173182] WOS Research Area Mathematics WOS Subject Statistics & Probability WOS ID WOS:000423887100004 Publisher ELSEVIER SCIENCE BV Citation statistics Cited Times:3[WOS]   [WOS Record]     [Related Records in WOS] Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/29470 Collection 应用数学研究所 Affiliation Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China Recommended CitationGB/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