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arXiv · 1501.06212

A Dimension Spectrum for SLE Boundary Collisions

Tom Alberts·Ilia Binder·Fredrik Johansson Viklund
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Abstract

We consider chordal SLE(kappa) curves for kappa > 4, where the intersection of the curve with the boundary is a random fractal of almost sure Hausdorff dimension min {2-8/kappa,1}. We study the random sets of points at which the curve collides with the real line at a specified "angle" and compute an almost sure dimension spectrum describing the metric size of these sets. We work with the forward SLE flow and a key tool in the analysis is Girsanov's theorem, which is used to study events on which moments concentrate. The two-point correlation estimates are proved using the direct method.

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Tom Alberts, Ilia Binder, Fredrik Johansson Viklund. 2015-02-28. A Dimension Spectrum for SLE Boundary Collisions. https://doi.org/10.1007/s00220-016-2587-x

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