= Transience of chordal SLE
{c}
The chordal <SLE> <Loewner trace> eventually leaves every bounded subset of the <complex upper half-plane>. For $0<\kappa<4$, its time-one <compact H-hull> is a simple slit and does not contain a half-disc. Instead, the <boundary approach forces a small SLE Bessel gap> estimate shows that every fixed nonzero real point is outside the closure of the full <Loewner trace>. After mapping out the initial simple slit, the starting point has two distinct real <prime end> images. A fresh independent <SLE> avoids approaching either image, so the original future stays a positive distance from its starting point. <Scaling invariance of SLE> gives $\inf_{t\geq T}|\gamma(t)|\overset d=\sqrt T\inf_{t\geq1}|\gamma(t)|$, and decreasing-event continuity proves escape from every fixed disc. The separate argument based on a swallowed half-disc at positive time applies in the nonsimple regime $\kappa>4$; it must not be applied to a simple slit. The critical parameters require their own limiting or trace-existence arguments.
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