Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 203 / 3 / c / ii / Solution

The imaginary partis a bounded local martingale and hence a martingale. As the simple transient trace passes $z$, this angle converges to $\pi$ if the trace passes to the right of $z$ and to $0$ if it passes to the left. Bounded convergence therefore givesso the SLE4 left-passage probability is