 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 $\kappa \ge 0$. 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.