RESUMEN
In this paper we present an analytic method for calculating the transition probability between two random Gaussian matrices with given eigenvalue spectra in the context of Dyson Brownian motion. We show that in the Coulomb gas language, in large N limit, memory of the initial state is preserved in the form of a universal linear potential acting on the eigenvalues. We compute the likelihood of any given transition as a function of time, showing that as memory of the initial state is lost, transition probabilities converge to those of the static ensemble.
RESUMEN
We propose a new field theory mechanism for generating an effective trans-Planckian decay constant from sub-Planckian ones. Using the minimal two axions and a hierarchy between two axion decay constants is sufficient for realizing inflation through nonperturbative effects only and with minimal tuning. The inflationary motion is kept entirely within a sub-Planckian domain. We outline possible strategies of embedding the model in a string theory setup.