Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 220 / 4 / b / Solution

The Locality property of SLE says the following. Let $D\subset \mathbb{H}$ be simply connected and agree with $\mathbb{H}$ in a neighborhood of $0$, and let $\psi :D\to \mathbb{H}$ be conformal with $\psi (0)=0$. The image under $\psi$ of an ${\mathrm{SLE}}_6$ in $\mathbb{H}$, stopped when it first leaves $D$, has the law of an ${\mathrm{SLE}}_6$ in $\mathbb{H}$, up to the corresponding stopping time and a change of half-plane-capacity parameterization.