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Multi-arm incipient infinite clusters in 2D: Scaling limits and winding numbers
Yao, Chang-Long
2018-11-01
Source PublicationANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES
ISSN0246-0203
Volume54Issue:4Pages:1848-1876
AbstractWe 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.
KeywordPercolation Scaling limit SLE CLE Incipient infinite cluster Winding number
DOI10.1214/17-AIHP858
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:000447616800005
PublisherINST MATHEMATICAL STATISTICS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/31345
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. 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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