  We consider a class of parabolic semi-linear stochastic partial differential
equations driven by space-time white noise on a compact space interval. Our aim
is to obtain precise asymptotics of the transition times between metastable
states. A version of the so-called Eyring-Kramers Formula is proven in an
infinite dimensional setting. The proof is based on a spatial finite difference
discretization of the stochastic partial differential equation. The expected
transition time is computed for the finite dimensional approximation and
controlled uniformly in the dimension.
