The scaling limit of a particle system with long-range interaction

We describe the macroscopic behaviour of a coupled bistable particle system where a large number of particles interact with each other.
Due to the properties of the driving force and the noise, the scaling limit does not lead in general to a well-posed equation. We develop conditions on the interaction strength between the particles to ensure existence of solutions to the limiting stochastic PDE. As a corollary we obtain that the metastable behaviour of the system under investigation is described by the Stochastic Allen Cahn equation, for which precise estimates on the transition time are available.
This is joint work with Anton Bovier.