  We explore the super-horizon evolution of the two-point and three-point
correlation functions of the primordial density perturbation in
randomly-generated multi-field potentials. We use the Transport method to
evolve perturbations and give full evolutionary histories for observables.
Identifying the separate universe assumption as being analogous to a
geometrical description of light rays, we give an expression for the width of
the bundle, thereby allowing us to monitor evolution towards the adiabatic
limit, as well as providing a useful means of understanding the behaviour in
$f_NL$. Finally, viewing our random potential as a toy model of inflation in
the string landscape, we build distributions for observables by evolving
trajectories for a large number of realisations of the potential and comment on
the prospects for testing such models. We find the distributions for
observables to be insensitive to the number of fields over the range 2 to 6,
but that these distributions are highly sensitive to the scale of features in
the potential. Most sensitive to the scale of features is the spectral index,
with more than an order of magnitude increase in the dispersion of predictions
over the range of feature scales investigated. Least sensitive was the
non-Gaussianity parameter $f_NL$, which was consistently small; we found no
examples of realisations whose non-Gaussianity is capable of being observed by
any planned experiment.
