EXTREME NESTING IN THE CONFORMAL LOOP ENSEMBLE

• 成果类型: Article
• 署名作者: Miller, Jason; Watson, Samuel S.; Wilson, David B.
• 署名单位: Massachusetts Institute of Technology (MIT); Microsoft
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/14-AOP995
• 发表日期: 2016
• 页码: 1013-1052
• 关键词: random-cluster model; critical percolation; thick points; sle

摘要

The conformal loop ensemble CLE kappa with parameter 8/3 < kappa < 8 is the canonical conformally invariant measure on countably infinite collections of noncrossing loops in a simply connected domain. Given kappa and nu, we compute the almost-sure Hausdorff dimension of the set of points z for which the number of CLE loops surrounding the disk of radius epsilon centered at z has asymptotic growth nu log(1/epsilon) as epsilon -> 0. By extending these results to a setting in which the loops are given i.i.d. weights, we give a CLE-based treatment of the extremes of the Gaussian free field.