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Hausdorff Dimension of the SLE Curve Intersected with the Real Line

   
@article{EJP515,
	author = {Tom Alberts and Scott Sheffield},
	title = {Hausdorff Dimension of the SLE Curve Intersected with the Real Line},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {13},
	year = {2008},
	keywords = {SLE; Hausdorff dimension; Two-point hitting probability},
	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.},
	pages = {no. 40, 1166-1188},
	issn = {1083-6489},
	doi = {10.1214/EJP.v13-515},    
        url = {http://ejp.ejpecp.org/article/view/515}}