Hausdorff Dimension of the SLE Curve Intersected with the Real Line

Tom Alberts, Scott Sheffield⋆

Type: Article

Publication Date: 2008-01-01

Citations: 37

DOI: https://doi.org/10.1214/ejp.v13-515

Abstract

We establish an upper bound on the asymptotic probability of an $SLE(\kappa)$ curve hitting two small intervals on the real line as the interval width goes to zero, for the range $4 < \kappa < 8$. As a consequence we are able to prove that the random set of points in $R$ hit by the curve has Hausdorff dimension $2-8/\kappa$, almost surely.

Locations

Electronic Journal of Probability - View - PDF
arXiv (Cornell University) - View - PDF

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