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arXiv math/0512464math.PRmath-phmath.MP
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连续质点系统随机动力学的N/V极限

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

Martin Grothaus, Yuri G. Kondratiev, Michael Röckner

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

本文给出了$\mathbb R^d$，$d \ge 1$上连续粒子系统中与Gibbs态相关的无限粒子、无限体积随机动力学的$N/V$极限.本文的出发点是一个具有奇异相互作用和反射边界条件的$N$ -粒子随机动力学问题，它是在一个具有有限体积（勒贝格测度）$V = |Λ| < \infty$的子集$Λ\subset {\mathbb R}^d$中进行的。目的是通过上述$N$ -$Λ$中的粒子动力学作为$N \to \infty$和$V \to \infty$来近似无限粒子、无限体积随机动力学，使得$N/V \to ρ$，其中$ρ$是粒子密度。

英文摘要：

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 $Λ\subset {\mathbb R}^d$ with finite volume (Lebesgue measure) $V = |Λ| < \infty$. The aim is to approximate the infinite particle, infinite volume stochastic dynamic by the above $N$-particle dynamic in $Λ$ as $N \to \infty$ and $V \to \infty$ such that $N/V \to ρ$, where $ρ$ is the particle density.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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