Limit theorems for critical first-passage percolation on the triangular lattice
文献类型：期刊论文
| 作者 | Yao, Chang-Long
|
| 刊名 | STOCHASTIC PROCESSES AND THEIR APPLICATIONS
 |
| 出版日期 | 2018-02-01 |
| 卷号 | 128期号:2页码:445-460 |
| 关键词 | Critical percolation First-passage percolation Scaling limit Conformal loop ensemble Law of large numbers Central limit theorem |
| ISSN号 | 0304-4149 |
| DOI | 10.1016/j.spa.2017.05.002 |
| 英文摘要 | 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. |
| 语种 | 英语 |
| WOS记录号 | WOS:000423887100004 |
| 出版者 | ELSEVIER SCIENCE BV |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/29469]  |
| 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. 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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