# The Green function for the radial Schramm-Loewner evolution

Tom Alberts,
Michael Kozdron,
Gregory Lawler

November 2012
SLE

### Abstract

We prove the existence of the Green function for radial SLE$(\kappa)$ for $\kappa < 8$. Unlike the chordal case where an explicit formula for the Green function is known for all values of $\kappa < 8$, we give an explicit formula only for $\kappa = 4$. For other values of $\kappa$, we give a formula in terms of an expectation with respect to SLE conditioned to go through a point.