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

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

2005-12-20

arxiv.org/abs/math/0512464v1

Mathematics

Probability

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

Scientific paper

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.

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