Hausdorff Dimension of the SLE Curve Intersected with the Real Line

@article{Alberts2007HausdorffDO,
  title={Hausdorff Dimension of the SLE Curve Intersected with the Real Line},
  author={Tom Alberts and Scott Sheffield},
  journal={Electronic Journal of Probability},
  year={2007},
  volume={13},
  pages={1166-1188}
}
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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