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May 2013 Multi-point Green’s functions for SLE and an estimate of Beffara
Gregory F. Lawler, Brent M. Werness
Ann. Probab. 41(3A): 1513-1555 (May 2013). DOI: 10.1214/11-AOP695

Abstract

In this paper we define and prove of the existence of the multi-point Green’s function for $\mbox{SLE}$—a normalized limit of the probability that an $\mbox{SLE}_{\kappa}$ 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 $\mbox{SLE}$. One of the main components to our proof is a refinement of a bound first provided by Beffara [Ann. Probab. 36 (2008) 1421–1452]. This work contains a proof of this bound independent from the original.

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Gregory F. Lawler. Brent M. Werness. "Multi-point Green’s functions for SLE and an estimate of Beffara." Ann. Probab. 41 (3A) 1513 - 1555, May 2013. https://doi.org/10.1214/11-AOP695

Information

Published: May 2013
First available in Project Euclid: 29 April 2013

zbMATH: 1277.60134
MathSciNet: MR3098683
Digital Object Identifier: 10.1214/11-AOP695

Subjects:
Primary: 60J67
Secondary: 82B27

Keywords: Green’s function , Schramm–Loewner evolutions

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.41 • No. 3A • May 2013
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