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#### Probabilitymathscidoc:1707.28001

Probab. Theorey Relat. Fields, (167), 45-105, 2017.1
We compute the almost-sure Hausdorff dimension of the double points of chordal SLE$_\kappa$ for $\kappa > 4$, 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 SLE$_\kappa$ for $\kappa > 4$ as well as analogous dimensions for the radial and whole-plane SLE$_\kappa(\rho)$ processes for $\kappa > 0$. 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 $e^{ih/\chi}$, where $h$ is a Gaussian free field and $\chi > 0$, of different angles with each other and with the domain boundary.
Schramm Loewner Evolution (SLE), Hausdorff dimension, double points, cut points, Gaussian Free Field (GFF), Imaginary Geometry
@inproceedings{hao2017intersection,
title={Intersection of SLE Paths: the double and cut point dimension of SLE},
author={Hao Wu, and Jason Miller},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170717102624338619794},
booktitle={Probab. Theorey Relat. Fields},
number={167},
pages={45-105},
year={2017},
}

Hao Wu, and Jason Miller. Intersection of SLE Paths: the double and cut point dimension of SLE. 2017. In Probab. Theorey Relat. Fields. pp.45-105. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170717102624338619794.