| 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 \({{\rm min}\{2-8/\kappa,1\}}\). 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. |
