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

Gregory F. Lawler ^[1] ; Brent M. Werness ^[1]
1. [1] University of Chicago
  
  University of Chicago
  
  City of Chicago, Estados Unidos
Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 41, Nº. 3, 1, 2013, págs. 1513-1555
Idioma: inglés
DOI: 10.1214/11-AOP695
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Resumen
- 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 SLEκ curve passes near to a pair of marked points in the interior of a domain. When κ<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) 1421–1452]. This work contains a proof of this bound independent from the original.