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arXiv:0711.4070 [math.PR]AbstractReferencesReviewsResources

Hausdorff dimension of the SLE curve intersected with the real line

Tom Alberts, Scott Sheffield

Published 2007-11-26Version 1

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 SLE curve intersected with the real line has Hausdorff dimension 2-8/kappa, almost surely.

Comments: 24 pages, 9 figures
Journal: Electron. Jour. Probab., 13:1166-1188 (electronic), 2008
Categories: math.PR
Subjects: 60D05, 60K35, 28A80
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