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

被引：35

作者：

Miller, Jason ^{[1
,2
]}

Wu, Hao ^{[1
,2
]}

机构：

[1] Univ Cambridge, Dept Pure Math & Math Stat, Stat Lab, Cambridge, England

[2] Univ Geneva, Sect Math, NCCR SwissMAP, Geneva, Switzerland

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2017年 / 167卷 / 1-2期

基金：

美国国家科学基金会;

关键词：

Schramm-Loewner evolution (SLE); Hausdorff dimension; Double points; Cut points; Gaussian free field (GFF); Imaginary geometry; UNIFORM SPANNING-TREES; ERASED RANDOM-WALKS; GAUSSIAN FREE-FIELD; CONFORMAL-INVARIANCE; PLANE EXPONENTS; CHORDAL SLE; DUALITY; VALUES; COUPLINGS; CURVE;

D O I：

10.1007/s00440-015-0677-x

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：45 / 105

页数：61

共 46 条

[1] Hausdorff dimension of the SLE curve intersected with the real line [J].