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arXiv · 1905.11307

A multifractal boundary spectrum for SLE$_κ(ρ)$

Lukas Schoug
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Abstract

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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BibTeXRIS

Lukas Schoug. 2020-06-17. A multifractal boundary spectrum for SLE$_κ(ρ)$. https://doi.org/10.1007/s00440-020-00975-w

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