Multi-arm incipient infinite clusters in 2D: Scaling limits and winding numbers | |
Yao, Chang-Long | |
刊名 | ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES |
2018-11-01 | |
卷号 | 54期号:4页码:1848-1876 |
关键词 | Percolation Scaling limit SLE CLE Incipient infinite cluster Winding number |
ISSN号 | 0246-0203 |
DOI | 10.1214/17-AIHP858 |
英文摘要 | We study the alternating k-arm incipient infinite cluster (IIC) of site percolation on the triangular lattice T. Using Camia and Newman's result that the scaling limit of critical site percolation on T is CLE6, we prove the existence of the scaling limit of the k-arm IIC for k = 1, 2, 4. Conditioned on the event that there are open and closed arms connecting the origin to partial derivative D-R, we show that the winding number variance of the arms is (3/2+ o(1)) log R as R -> 8, which confirms a prediction of Wieland and Wilson [Phys. Rev. E 68 (2003) 056101]. Our proof uses two-sided radial SLE6 and coupling argument. Using this result we get an explicit form for the CLT of the winding numbers, and get analogous result for the 2-arm IIC, thus improving our earlier result. |
语种 | 英语 |
出版者 | INST MATHEMATICAL STATISTICS |
WOS记录号 | WOS:000447616800005 |
内容类型 | 期刊论文 |
源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/31344] |
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. Multi-arm incipient infinite clusters in 2D: Scaling limits and winding numbers[J]. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES,2018,54(4):1848-1876. |
APA | Yao, Chang-Long.(2018).Multi-arm incipient infinite clusters in 2D: Scaling limits and winding numbers.ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES,54(4),1848-1876. |
MLA | Yao, Chang-Long."Multi-arm incipient infinite clusters in 2D: Scaling limits and winding numbers".ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES 54.4(2018):1848-1876. |
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