Reversibility of whole-plane SLE

• 成果类型: Article
• 署名作者: Zhan, Dapeng
• 署名单位: Michigan State University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-014-0554-z
• 发表日期: 2015
• 页码: 561-618
• 关键词: erased random-walks; conformal-invariance; RESTRICTION; Duality

摘要

The main result of this paper is that, for , whole-plane SLE satisfies reversibility, which means that the time-reversal of a whole-plane SLE trace is still a whole-plane SLE trace. In addition, we find that the time-reversal of a radial SLE trace for is a disc SLE 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 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.