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We explore the super-horizon evolution of the two-point and three-pointcorrelation functions of the primordial density perturbation inrandomly-generated multi-field potentials. We use the Transport method toevolve perturbations and give full evolutionary histories for observables.Identifying the separate universe assumption as being analogous to ageometrical description of light rays, we give an expression for the width ofthe bundle, thereby allowing us to monitor evolution towards the adiabaticlimit, 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 inthe string landscape, we build distributions for observables by evolvingtrajectories for a large number of realisations of the potential and comment onthe prospects for testing such models. We find the distributions forobservables 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 inthe potential. Most sensitive to the scale of features is the spectral index,with more than an order of magnitude increase in the dispersion of predictionsover the range of feature scales investigated. Least sensitive was thenon-Gaussianity parameter $f_NL$, which was consistently small; we found noexamples of realisations whose non-Gaussianity is capable of being observed byany planned experiment.

Multi-field inflation with random potentials: field dimension, feature scale and non-Gaussianity