Abstract
We study {{,mathrm{SLE},}}_kappa (rho ) curves, with kappa and rho 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 g_t, by employing the Girsanov theorem and using imaginary geometry techniques to derive a correlation estimate.
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