| Abstract: |
| We study the Allen-Cahn equation perturbed by a small space-time white noise. It is by now well known that if the space dimension is larger than one such a white noise driven equation has to be interpreted in a renormalised sense, i.e. formally infinite counter-terms have to be added to make sense of the solution.
In this talk I will discuss the small noise behaviour of this renormalised SPDE. I will discuss the validity of the Kramers-Eyring law, which gives a precise description of the asymptotic expected transition times between meta-stable states in the small noise limit. An important part of the proof is a synchronisation result, which states that two solutions which start nearby will never separate with overwhelming probability. |
|