The Vlasov dynamics and its fluctuations in the \(1/N\) limit of interacting classical particles. (English) Zbl 1155.81383

Summary: For classical \(N\)-particle systems with pair interaction \(N^{-1} \sum \limits_{1 \leqq i \leqq j \leqq N} \phi(q_i-q_i)\) the Vlasov dynamics is shown to be the \(w^*\)-limit as \(N\to\infty\). Propagation of molecular chaos holds in this limit, and the fluctuations of intensive observables converge to a Gaussian stochastic process.


81V70 Many-body theory; quantum Hall effect
82C22 Interacting particle systems in time-dependent statistical mechanics
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