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

被引：24
|
作者：
Lawler, Gregory F. [1 ]
Werness, Brent M. [1 ]
机构：
[1] Univ Chicago, Dept Math, Chicago, IL 60637 USA
来源：
ANNALS OF PROBABILITY | 2013年 / 41卷 / 3A期
基金：
美国国家科学基金会;
关键词：
UNIFORM SPANNING-TREES; ERASED RANDOM-WALKS; CONFORMAL-INVARIANCE; SCALING LIMITS;
D O I：
10.1214/11-AOP695
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
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.
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页码：1513 / 1555
页数：43
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