  We construct a class of random potentials for N >> 1 scalar fields using
non-equilibrium random matrix theory, and then characterize multifield
inflation in this setting. By stipulating that the Hessian matrices in adjacent
coordinate patches are related by Dyson Brownian motion, we define the
potential in the vicinity of a trajectory. This method remains computationally
efficient at large N, permitting us to study much larger systems than has been
possible with other constructions. We illustrate the utility of our approach
with a numerical study of inflation in systems with up to 100 coupled scalar
fields. A significant finding is that eigenvalue repulsion sharply reduces the
duration of inflation near a critical point of the potential: even if the
curvature of the potential is fine-tuned to be small at the critical point,
small cross-couplings in the Hessian cause the curvature to grow in the
neighborhood of the critical point.
