The Scaling Limit of a Particle System with Long-Range Interaction

#### A. Bovier, C. Geldhauser

2017, v.23, Issue 4, 515-552

ABSTRACT

We describe the behaviour of a particle system with long-range interactions, in which the range of interactions is allowed to depend on the size of the system. We give conditions on the interaction strength under which the scaling limit of the particle system is a well-posed stochastic PDE. As a corollary we obtain that the metastable behaviour of the system is described by the Stochastic Allen\tire Cahn equation, which has been analyzed by Barret, Bovier and Meleard, Barret and Berglund and Gentz.

Keywords: metastability; metastable transition time; parabolic stochastic partial differential equations; reaction-diffusion equations