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Title: Rejecting the mean-field hypothesis Abstract: Given the partial observation of several interacting particles over a limited time horizon, we explore the following question: do all particles interact in the same way, or is there a characteristic scale beyond which the particles cannot statistically significantly see the effect of the other particles? We construct an asymptotically optimal test for the null: "the particles are in a mean-field regime" against a set of local alternatives: "the interaction range collapses in a hydrodynamic limit at a certain rate". We identify the optimal separation rate in a minimax sense. Our results build on recent results of quantitative propagation of chaos for moderately interacting particle systems and more classical results inspired by nonparametric estimation of quadratic functionals. Joint work with Žarko Bulić (Oxford).

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