A multifractal boundary spectrum for SLE κ ( ρ )
Abstract: We study SLEκ(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 dimensions of these sets. This is done by studying the moments of the spatial derivatives of the conformal maps gt, by employing the Girsanov theorem and using imaginary geometry techniques to derive a correlation estimate.
Funder: University of Cambridge