  We study the anisotropic version of the Hastings-Levitov model AHL$(\nu)$.
Previous results have shown that on bounded time-scales the harmonic measure on
the boundary of the cluster converges, in the small-particle limit, to the
solution of a deterministic ordinary differential equation. We consider the
evolution of the harmonic measure on time-scales which grow logarithmically as
the particle size converges to zero and show that, over this time-scale, the
leading order behaviour of the harmonic measure becomes random. Specifically,
we show that there exists a critical logarithmic time window in which the
harmonic measure flow, started from the unstable fixed point, moves
stochastically from the unstable point towards a stable fixed point, and we
show that the full trajectory can be characterised in terms of a single
Gaussian random variable.
