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Hausdorff Dimension of the SLE Curve Intersected with the Real Line
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Tom Alberts, Courant Institute of Mathematical Sciences
Scott Sheffield, Courant Institute of Mathematical Sciences
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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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Full text: PDF
Pages: 1166-1188
Published on: July 29, 2008
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Electronic Journal of Probability. ISSN: 1083-6489 |
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