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

Understand

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 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.