MULTI-POINT GREEN'S FUNCTIONS FOR SLE AND AN ESTIMATE OF BEFFARA

• 成果类型: Article
• 署名作者: Lawler, Gregory F.; Werness, Brent M.
• 署名单位: University of Chicago
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP695
• 发表日期: 2013
• 页码: 1513-1555
• 关键词: uniform spanning-trees; erased random-walks; conformal-invariance; SCALING LIMITS

摘要

In this paper we define and prove of the existence of the multi-point Green's function for SLE a normalized limit of the probability that an SLE kappa curve passes near to a pair of marked points in the interior of a domain. When kappa <8 this probability is nontrivial, and an expression can be written in terms two-sided radial SLE. One of the main components to our proof is a refinement of a bound first provided by Beffara [Ann. Probab. 36 (2008) 14211452]. This work contains a proof of this bound independent from the original.