= SLE does not hit a fixed nonzero boundary point
{c}
{title2=$0\leq\kappa<8$}
For a fixed $x\in\mathbb R\setminus\{0\}$, a chordal <SLE> trace in $(\mathbb H,0,\infty)$ satisfies
$$
\mathbb P\{x\in\gamma[0,\infty)\}=0\qquad(0\leq\kappa<8).
$$
For $\kappa\leq4$ the trace avoids the entire nonzero real boundary. For $4<\kappa<8$ it meets a random boundary <subset> but misses each predetermined <point>. A fixed <point> is nevertheless swallowed almost surely in this latter range: visiting and disconnecting from infinity are different events.<Basic properties of SLE by Steffen Rohde and Oded Schramm>[Section 6, Theorem 6.1, Lemma 6.6 and proof of Theorem 6.4, printed pp. 23 and 30–31]{ref}
The restriction $\kappa<8$ is essential. At $\kappa\geq8$, the <strict ordering threshold for SLE boundary swallowing> and <real-line visitation from strict SLE swallowing order> give visits to every real boundary <point>. The <SLE boundary-point logarithmic separation diffusion> proves the below-eight fixed-point assertion through the <probability> of swallowing before a nearby <point>; its limiting behavior changes at eight.
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