Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 203 / 3 / d / ii / Solution

Fix $R>0$. Part i, with $ϵ$ arbitrarily small and $t$ sufficiently large, shows thatThe hulls increase with time. Once this half-disc lies in $K_t$, the stated future-avoidance property givesIntersecting these probability-one events over positive integer $R$ provesalmost surely. This is Transience of chordal SLE.