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

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

2010-11-15

arxiv.org/abs/1011.3551v3

Mathematics

Probability

Scientific paper

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 non-trivial, 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. This work contains a proof of this bound independent from the original.

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