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Abstract: The main result of this paper is that, for $\kappa\in0,4$, whole-planeSLE$ \kappa$ satisfies reversibility, which means that the time-reversal of awhole-plane SLE$ \kappa$ trace is still a whole-plane SLE$ \kappa$ trace. Inaddition, we find that the time-reversal of a radial SLE$ \kappa$ trace for$\kappa\in0,4$ is a disc SLE$ \kappa$ trace with a marked boundary point. Themain tool used in this paper is a stochastic coupling technique, which is usedto couple two whole-plane SLE$ \kappa$ traces so that they overlap. Anothertool used is the Feynman-Kac formula, which is used to solve a PDE. Thesolution of this PDE is then used to construct the above coupling.



Author: Dapeng Zhan

Source: https://arxiv.org/



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