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A multifractal boundary spectrum for SLE$_κ(ρ)$
Lukas Schoug · 2019-05-27 · via math.PR updates on arXiv.org

We study SLE$_κ(ρ)$ curves, with $κ$ and $ρ$ chosen so that the curves hit the boundary. More precisely, we study the sets on which the curves collide with the boundary at a prescribed "angle" and determine the almost sure Hausdorff dimension of these sets. This is done by studying the moments of the spatial derivatives of the conformal maps $g_t$, by employing the Girsanov theorem and using imaginary geometry techniques to derive a correlation estimate.

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