A dimension spectrum for SLE boundary collisions
The authors consider a multifractal spectrum describing the fine geometry of the Schramm-Loewner evolution \((\mathrm{SLE}_k, k>4)\) curves, where the intersection of the curve with the boundary is a random fractal of almost sure Hausdorff dimension \(\min\{2-8/k,1\}\). It is proved that this fractal can be decomposed into a family of sets of smaller dimensions according to the ``angle'' at which the curve hits the boundary. Two-point correlation estimates are proved using the direct method.
scientific article; zbMATH DE number 6571699
scientific article