Ergodicity of the tip of an SLE curve

• 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/s00440-014-0613-5
• 发表日期: 2016
• 页码: 333-360
• 关键词: scaling limits

摘要

We first prove that, for kappa is an element of (0, 4), a whole-plane SLE(kappa; kappa + 2) trace stopped at a fixed capacity time satisfies reversibility. We then use this reversibility result to prove that, for kappa is an element of(0, 4), a chordal SLE kappa curve stopped at a fixed capacity time can be mapped conformally to the initial segment of a whole-plane SLE(kappa; kappa+ 2) trace. A similar but weaker result holds for radial SLE.. These results are then used to study the ergodic behavior of an SLE curve near its tip point at a fixed capacity time. The proofs rely on the symmetry of backward SLE weldings and conformal removability of SLE kappa curves for kappa is an element of (0, 4).