Hausdorff Dimension of the SLE Curve Intersected with the Real Line
Scott Sheffield (Courant Institute of Mathematical Sciences)
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.
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Pages: 1166-1188
Publication Date: July 29, 2008
DOI: 10.1214/EJP.v13-515
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