Reversibility of Whole-Plane SLE

Dapeng Zhan

Reversibility of Whole-Plane SLE

Probability 2013-05-17 v3

Authors: Dapeng Zhan

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.

Keywords

whole-plane SLE reversibility radial SLE stochastic coupling Feynman-Kac formula

Cite

@article{arxiv.1004.1865,
  title  = {Reversibility of Whole-Plane SLE},
  author = {Dapeng Zhan},
  journal= {arXiv preprint arXiv:1004.1865},
  year   = {2013}
}

Comments

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

Reversibility of Whole-Plane SLE

Abstract

Keywords

Cite

Comments

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