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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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

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

First available in Project Euclid: 29 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Schramm–Loewner evolutions Green’s function


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.

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