N/V-limit for Stochastic Dynamics in Continuous Particle Systems

Abstract

We provide an $N/V$-limit for the infinite particle, infinite volume stochastic dynamics associated with Gibbs states in continuous particle systems on ${\mathbb{R}}^d$, $d\ge 1$. Starting point is an $N$-particle stochastic dynamic with singular interaction and reflecting boundary condition in a subset $\Lambda \subset {\mathbb{R}}^d$ with finite volume (Lebesgue measure) $V=|\Lambda |<\infty$. The aim is to approximate the infinite particle, infinite volume stochastic dynamic by the above $N$-particle dynamic in $\Lambda$ as $N\to \infty$ and $V\to \infty$ such that $N/V\to \rho$, where $\rho$ is the particle density.

35 pages; BiBoS-Preprint No. 04-12-172; publication in preparation