Random Matrices and the Spectrum of N-flation

N-flation is a promising embedding of inflation in string theory in which many string axions combine to drive inflation. We characterize the dynamics of a general N-flation model with non-degenerate axion masses. Although the precise mass of a single axion depends on compactification details in a complicated way, the distribution of masses can be computed with very limited knowledge of microscopics: the shape of the mass distribution is an emergent property. We use random matrix theory to show that a typical N-flation model has a spectrum of masses distributed according to the Marchenko-Pastur law. This distribution depends on a single parameter, the number of axions divided by the dimension of the moduli space. We use this result to describe the inflationary dynamics and phenomenology of a general N-flation model. We produce an ensemble of models and use numerical integration to track the axions' evolution and the resulting scalar power spectrum. For realistic initial conditions, the power spectrum is considerably more red than in single-field $m^2\phi^2$ inflation. We conclude that random matrix models of N-flation are surprisingly tractable and have a rich phenomenology that differs in testable ways from that of single-field $m^2\phi^2$ inflation.