The authors consider mean-field measures with interacting potential . The probability measure is the law of an interacting system of size . The authors are interested in the asymptotic independence properties of these measures, as tends to infinity. This asymptotic behavior is called asymptotic chaoticity. Under mild assumptions, one proves that the empirical measures of the system converge in law to a deterministic measure , and equivalently for any finite , the convergence of the law of -subsystem under to .
The authors estimate the relative entropy distance between and appropriate simpler exchangeable measures which are related to the law . They prove that if the minimum of the function is unique, say , then , and propagation of chaos holds for blocks of size if this minimum is nondegenerate. Certain degenerate situations are also studied. Next these results are applied to the Langevin dynamics of interacting particles leading to a McKean-Vlasov limit.