Hausdorff dimension of the SLE curve intersected with the real line

Tom Alberts; Scott Sheffield

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arXiv · 0711.4070

Hausdorff dimension of the SLE curve intersected with the real line

Tom Alberts·Scott Sheffield

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

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Tom Alberts, Scott Sheffield. 2007-11-26. Hausdorff dimension of the SLE curve intersected with the real line. https://arxiv.org/abs/0711.4070

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