= Solution
Stop after a positive initial segment and map it out. By the <Conformal Markov property of SLE>, the future is a fresh SLE in the remaining domain. Part b says that it hits that domain's boundary away from its current and terminal points. Choosing a bounded crosscut neighborhood whose real-boundary part is shielded from the future forces such a hit to occur on the image of the earlier trace with positive probability. Scale invariance and repeated conditional trials upgrade this to probability one. Thus the trace has self-intersections for $\kappa>4$, in agreement with the <Phase classification of the SLE trace>.
Back to article page
