= Scale-and-domain-Markov characterization of SLE
Among <Loewner chains> with capacity $2t$, continuous real driver and initial driver zero, scale invariance and the centered <domain Markov property of a chordal Loewner chain> characterize <Schramm–Loewner evolution> with some $\kappa\geq0$. <Driving-function reconstruction for a chordal Loewner chain> turns the hull properties into stationary independent increments and Brownian scaling for the driver. The <continuous Lévy process> classification then gives $U_t=bt+\sqrt\kappa W_t$, and scaling eliminates $b$. Regularity and parametrization are essential hypotheses of this characterization.
Back to article page
