N/v -limit for Langevin Dynamics in Continuum

We construct an infinite particle/infinite volume Langevin dynamics on the space of configurations in R having velocities as marks. The construction is done via a limiting procedure using N-particle dynamics in cubes (−λ, λ] with periodic boundary conditions. A main step to this result is to derive an (improved) Ruelle bound for the canonical correlation functions of N-particle systems in (−λ, λ] with periodic boundary conditions. After proving tightness of the laws of finite particle dynamics, the identification of accumulation points as martingale solutions of the Langevin equation is based on a general study of properties of measures on configuration space (and their weak limit) fulfilling a uniform Ruelle bound. Additionally, we prove that the initial/invariant distribution of the constructed dynamics is a tempered grand canonical Gibbs measure. All proofs work for general repulsive interaction potentials φ of Ruelle type (e.g. the Lennard-Jones potential) and all temperatures, densities and dimensions d ≥ 1.