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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.

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