A multifractal boundary spectrum for SLEκ (ρ)

• 成果类型: Article; Early Access
• 署名作者: Schoug, Lukas
• 署名单位: University of Cambridge
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-020-00975-w
• 发表日期: 2020
• 关键词: dimension; reversibility; curve; tip

摘要

We study SLE kappa (rho) curves, with kappa and rho chosen so that the curves hit the boundary. More precisely, we study the sets on which the curves collide with the boundary at a prescribed angle and determine the almost sure Hausdorff dimensions of these sets. This is done by studying the moments of the spatial derivatives of the conformal maps g(t), by employing the Girsanov theorem and using imaginary geometry techniques to derive a correlation estimate.