Intersections of SLE Paths: the double and cut point dimension of SLE
Probability
2013-03-20 v1 Mathematical Physics
Complex Variables
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.1303.4725,
title = {Intersections of SLE Paths: the double and cut point dimension of SLE},
author = {Jason Miller and Hao Wu},
journal= {arXiv preprint arXiv:1303.4725},
year = {2013}
}
Comments
70 page, 26 figures