Reversibility of Whole-Plane SLE

Abstract

The main result of this paper is that, for $\kappa\in(0,4]$, whole-plane SLE$_\kappa$ satisfies reversibility, which means that the time-reversal of a whole-plane SLE$_\kappa$ trace is still a whole-plane SLE$_\kappa$ trace. In addition, we find that the time-reversal of a radial SLE$_\kappa$ trace for $\kappa\in(0,4]$ is a disc SLE$_\kappa$ trace with a marked boundary point. The main tool used in this paper is a stochastic coupling technique, which is used to couple two whole-plane SLE$_\kappa$ traces so that they overlap. Another tool used is the Feynman-Kac formula, which is used to solve a PDE. The solution of this PDE is then used to construct the above coupling.