  There is considerable interest in inflationary models with multiple inflaton
fields. The inflaton field $\boldsymbol\phi$ that has been postulated to drive
accelerating expansion in the very early universe has a corresponding potential
$V$, the details of which are free parameters of the theory. We consider a
natural hypothesis that $V$ ought to be maximally random. We realize this idea
by defining $V$ as a Gaussian random field in some number $N$ of dimensions.
Given a model that statistically determines the shape of $V$, we repeatedly
evolve $\boldsymbol\phi$ under random potentials, cataloging a representative
sample of trajectories associated with that model. On anthropic grounds, we
impose a minimum with $V=0$ and only consider trajectories that reach that
minimum. We simulate each path evolution stepwise through
$\boldsymbol\phi$-space while simultaneously computing $V$ and its derivatives
along the path via a Gaussian random process. When $N$ is large, this method
significantly reduces computational load as compared to methods that generate
the potential landscape all at once. Even so, the covariance matrix of
constraints on $V$ can quickly become large and cumbersome. To solve this
problem, we present data compression algorithms to prioritize the necessary
information already simulated, then keep an arbitrarily large portion. With
these optimizations, we simulate thousands of trajectories, extract matter,
tensor, and isocurvature spectra from each, and then assemble statistical
predictions of these quantities through repeated trials. We find that the
Gaussian random potential is a highly versatile inflationary model with a rich
volume of parameter space capable of reproducing modern observations.
