  We evaluate the steady-state distribution and escape rate for an Active
Ornstein-Uhlenbeck Particle (AOUP) using methods from the theory of large
deviations. The calculation is carried out both for small and large memory
times of the active force in one-dimension. We compare our results to those
obtained in the literature about colored noise processes, and we emphasize
their relevance for the field of active matter. In particular, we stress that
contrary to equilibrium particles, the invariant measure of such an active
particle is a non-local function of the potential. This fact has many
interesting consequences, which we illustrate through two phenomena. First,
active particles in the presence of an asymmetric barrier tend to accumulate on
one side of the potential -a ratchet effect that was missing is previous
treatments. Second, an active particle can escape over a deep metastable state
without spending any time at its bottom.
