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2008 Hausdorff Dimension of the SLE Curve Intersected with the Real Line
Tom Alberts, Scott Sheffield
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Electron. J. Probab. 13: 1166-1188 (2008). DOI: 10.1214/EJP.v13-515


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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Tom Alberts. Scott Sheffield. "Hausdorff Dimension of the SLE Curve Intersected with the Real Line." Electron. J. Probab. 13 1166 - 1188, 2008.


Accepted: 29 July 2008; Published: 2008
First available in Project Euclid: 1 June 2016

zbMATH: 1192.60025
MathSciNet: MR2430703
Digital Object Identifier: 10.1214/EJP.v13-515

Primary: 60D05
Secondary: 28A80 , 60K35

Keywords: Hausdorff dimension , SLE , Two-point hitting probability

Vol.13 • 2008
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