= Positive boundary-interval hitting probability for SLE above parameter four
For $\kappa>4$, the <Boundary-point Bessel flow for SLE> and the <SLE boundary swallowing criterion> imply that the full <Loewner trace> hits the positive real axis almost surely. Every fixed open interval in that axis has positive hitting probability: its countably many dilates cover the axis, while <Scaling invariance of SLE> makes all their hitting probabilities equal. Reflection gives the corresponding negative-axis statement. Together with the <domain Markov property of a chordal Loewner chain>, this produces visits to the old <Loewner trace> boundary in a mapped future domain.
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