Exit Time for a Reaction Diffusion Model
2004, v.10, Issue 4, 705-744
We consider an interacting particle system, the Glauber+Kawasaki model. This model is the result of the combination of a fast stirring, the Kawasaki part, and a spin flip process, the Glauber part. This process has a Reaction Diffusion equation as hydrodynamic limit. The ergodicity of this dynamics in the presence of a metastable state (double well potential) was recently proven, for any dimension. In this article we obtain the asymptotic exponential distribution of certain exit time from a subset of the basin of attraction of one of the wells.
Keywords: exit times,interacting particle systems,Glauber - Kawasakidynamics,Reaction Diffusion equations,hydrodynamic limits