  We construct models of inflation with many randomly interacting fields and
use these to study the generation of cosmological observables. We model the
potentials as multi-dimensional Gaussian random fields (GRFs) and identify
powerful algebraic simplifications that, for the first time, make it possible
to access the manyfield limit of inflation in GRF potentials. Focussing on
small-field, slow-roll, approximate saddle-point inflation in potentials with
structure on sub-Planckian scales, we construct explicit examples involving up
to 100 fields and generate statistical ensembles comprising of 164,000 models
involving 5 to 50 fields. For the subset of these that support at least sixty
e-folds of inflation, we use the 'transport method' and $\delta N$ formalism to
determine the predictions for cosmological observables at the end of inflation,
including the power spectrum and the local non-Gaussianities of the primordial
perturbations. We find three key results: i) Planck compatibility is not rare,
but future experiments may rule out this class of models; ii) In the manyfield
limit, the predictions from these models agree well with, but are sharper than,
previous results derived using potentials constructed through non-equilibrium
Random Matrix Theory; iii) Despite substantial multifield effects,
non-Gaussianities are typically very small: $f_{\rm nl}^{\rm loc} \ll 1$. We
conclude that many of the 'generic predictions' of single-field inflation can
be emergent features of complex inflation models.
