Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 203 / 1 / d / Solution

The parameterization in part (c) gives the exact self-similarityfor every $\lambda >0$. The Loewner local growth property supplies a continuous Loewner driving function $U$. Under this scaling of the hulls, the deterministic scaling rule for the Chordal Loewner equation givesTaking $t=1$ and $\lambda =\sqrt{t}$ shows thatfor the real constant $c=U_1$.