Florent Barret (Ecole Polytechnique)
Title: Metastability and transition times for a SPDE perturbed by space-time white noise in dimension 1 in space.
deal with the metastable behavior of the solution of a SPDE parabolic
and semilinear, the noise comes from a space-time white noise. This
equation could also be seen as the stochastic perturbation of a
gradient flow in infinite dimension. We are interested in the
asymptotics of the transition times between two minima of our action
functional as the intensity of the noise goes to 0. Previous works
(Jona-Lasinio, Faris...) showed that as in the finite dimensional case
(Freidlin-Wentzell theory) the transition time is asymptotically an
exponential random variable, logarithmic asymptotics of the expected
time are also known.
We prove in our settings, exact asymptotics of
the transition time through a finite difference approximation of our
equation (so-called Eyring-Kramers Formula). We apply finite
dimensional estimate (Bovier, Eckhoff, Gayrard, Klein) to the system
obtained and prove that we can control them uniformly in the dimension
(which equals the number of discretization points).