The Annals of Probability

Multi-point Green’s functions for SLE and an estimate of Beffara

Gregory F. Lawler and Brent M. Werness

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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.

Article information

Source
Ann. Probab., Volume 41, Number 3A (2013), 1513-1555.

Dates
First available in Project Euclid: 29 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aop/1367241505

Digital Object Identifier
doi:10.1214/11-AOP695

Mathematical Reviews number (MathSciNet)
MR3098683

Zentralblatt MATH identifier
1277.60134

Subjects
Primary: 60J67: Stochastic (Schramm-)Loewner evolution (SLE)
Secondary: 82B27: Critical phenomena

Keywords
Schramm–Loewner evolutions Green’s function

Citation

Lawler, Gregory F.; Werness, Brent M. Multi-point Green’s functions for SLE and an estimate of Beffara. Ann. Probab. 41 (2013), no. 3A, 1513--1555. doi:10.1214/11-AOP695. https://projecteuclid.org/euclid.aop/1367241505


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References

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