Duality of chordal SLE

• 成果类型: Article
• 署名作者: Zhan, Dapeng
• 署名单位: Yale University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-008-0132-z
• 发表日期: 2008
• 页码: 309-353
• 关键词: erased random-walks; conformal-invariance; SCALING LIMITS; plane

摘要

We derive some geometric properties of chordal SLE(k; (rho) over right arrow) processes. Using these results and the method of coupling two SLE processes, we prove that the outer boundary of the final hull of a chordal SLE(k; (rho) over right arrow) process has the same distribution as the image of a chordal SLE(k'; (rho) over right arrow) trace, where k > 4, k' = 16/k, and the forces (rho) over right arrow and (rho) over right arrow' are suitably chosen. We find that for. = 8, the boundary of a standard chordal SLE(.) hull stopped on swallowing a fixed x is an element of R\{0} is the image of some SLE(16/k; (rho) over right arrow) trace started from x. Then we obtain a new proof of the fact that chordal SLE(k) trace is not reversible for k > 8. We also prove that the reversal of SLE( 4; (rho) over right arrow) trace has the same distribution as the time- change of some SLE(4; (rho) over right arrow') trace for certain values of (rho) over right arrow and (rho) over right arrow'.