The conformal loop ensemble nesting field

• 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; Microsoft
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-014-0604-6
• 发表日期: 2015
• 页码: 769-801
• 关键词: random-cluster model

摘要

The conformal loop ensemble with parameter is the canonical conformally invariant measure on countably infinite collections of non-crossing loops in a simply connected domain. We show that the number of loops surrounding an -ball (a random function of and ) minus its expectation converges almost surely as to a random conformally invariant limit in the space of distributions, which we call the nesting field. We generalize this result by assigning i.i.d. weights to the loops, and we treat an alternate notion of convergence to the nesting field in the case where the weight distribution has mean zero. We also establish estimates for moments of the number of CLE loops surrounding two given points.