Schramm–Loewner Equations Driven by Symmetric Stable Processes

Abstract

We consider shape, size and regularity of the hulls K t of the chordal Schramm–Loewner evolution driven by a symmetric α-stable process. We obtain derivative estimates, show that the domains $${\mathbb{H}{\setminus}K_{t}}$$ are Hölder domains, prove that K t has Hausdorff dimension 1, and show that the trace is right-continuous with left limits almost surely.