  In this work we prove a Kramers' type law for the low-temperature behavior of
the exit-times from a metastable state for a class of self-interacting
nonlinear diffusion processes. Contrary to previous works, the interaction is
not assumed to be convex, which means that this result covers cases where the
exit-time for the interacting process is smaller than the exit-time for the
associated non-interacting process. The technique of the proof is based on the
fact that, under an appropriate contraction condition, the interacting process
is conveniently coupled with a non-interacting (linear) Markov process where
the interacting law is replaced by a constant Dirac mass at the fixed point of
the deterministic zero-temperature process.
