Past exam of the mathematics course of the University of Cambridge / 2014 / iii / Paper 29 / 2 / d / Solution

Substitute $R=r^{\pi /\alpha }$ from part (a) into part (c). The Brownian wedge-exit probability isIt tends to $1$ as $r\downarrow 1$, and is asymptotic to $(4/\pi )r^{-\pi /\alpha }$ as $r\to \infty$. The exponent reflects how the conformal map stretches wedge angles; wider wedges give slower decay.