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.

The current version has 54 pages. The previous version is shortened without losing the main results or its clarity. Some sections/subsections in the previous version were removed or combined to save the space. I also add more explanations to emphasize the ideas. arXiv admin note: text overlap with arXiv:0904.0808

References in corpus (3)

• Duality of Chordal SLE
• Defining SLE in multiply connected domains with the Brownian loop measure
• Duality of Chordal SLE, II

Cited by in corpus (4)

• Restriction Properties of Annulus SLE
• Backward SLE and the symmetry of the welding
• Ergodicity of the tip of an SLE curve
• SLE and Virasoro representations: localization