  We construct ensembles of random scalar potentials for $N_f$ interacting
scalar fields using non-equilibrium random matrix theory, and use these to
study the generation of observables during small-field inflation. For
$N_f={\cal O}({\rm few})$, these heavily featured scalar potentials give rise
to power spectra that are highly non-linear, at odds with observations. For
$N_f\gg 1$, the superhorizon evolution of the perturbations is generically
substantial, yet the power spectra simplify considerably and become more
predictive, with most realisations being well approximated by a linear power
spectrum. This provides proof of principle that complex inflationary physics
can give rise to simple emergent power spectra. We explain how these results
can be understood in terms of large $N_f$ universality of random matrix theory.
