Transience of chordal SLE

The chordal ${\mathrm{SLE}}_{\kappa }$ trace in $(\mathbb{H},0,\infty )$ satisfies $|\gamma (t)|\to \infty$ in the sense that it eventually leaves every bounded subset. Scaling invariance of SLE reduces this to a positive probability that the time-one hull contains a fixed half-disc, while the increasing-hull property and the Conformal Markov property of SLE turn that estimate into almost-sure escape.