The Green function for the radial Schramm–Loewner evolution

Abstract

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