Intersections of SLE Paths: the double and cut point dimension of SLE

• 成果类型: Article
• 署名作者: Miller, Jason; Wu, Hao
• 署名单位: University of Cambridge; University of Geneva
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-015-0677-x
• 发表日期: 2017
• 页码: 45-105
• 关键词: uniform spanning-trees; erased random-walks; gaussian free-field; conformal-invariance; plane exponents; chordal sle; Duality; VALUES; Couplings; curve

摘要

We compute the almost-sure Hausdorff dimension of the double points of chordal for , confirming a prediction of Duplantier-Saleur (1989) for the contours of the FK model. We also compute the dimension of the cut points of chordal for as well as analogous dimensions for the radial and whole-plane processes for . We derive these facts as consequences of a more general result in which we compute the dimension of the intersection of two flow lines of the formal vector field , where h is a Gaussian free field and , of different angles with each other and with the domain boundary.