  In this paper we study the fluctuations from the limiting behavior of small
noise random perturbations of diffusions with multiple scales. The result is
then applied to the exit problem for multiscale diffusions, deriving the
limiting law of the joint distribution of the exit time and exit location. We
apply our results to the first order Langevin equation in a rough potential,
studying both fluctuations around the typical behavior and the conditional
limiting exit law, conditional on the rare event of going against the
underlying deterministic flow.
