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arXiv · 1004.1865

Reversibility of Whole-Plane SLE

Dapeng Zhan
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Abstract

The main result of this paper is that, for $κ\in(0,4]$, whole-plane SLE$_κ$ satisfies reversibility, which means that the time-reversal of a whole-plane SLE$_κ$ trace is still a whole-plane SLE$_κ$ trace. In addition, we find that the time-reversal of a radial SLE$_κ$ trace for $κ\in(0,4]$ is a disc SLE$_κ$ 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$_κ$ 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.

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Dapeng Zhan. 2013-05-16. Reversibility of Whole-Plane SLE. https://arxiv.org/abs/1004.1865

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