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This article deals with a mean-field model. We consider a large number of particles interacting through their empirical law. We know that there is a unique invariant probability for this diffusion. We look at functional inequalities. In particular, we briefly show that the diffusion satisfies a Poincare inequality. Then, we establish a so-called WJ-inequality, which is independent from the number of particles.

Exponential rate of convergence independent of the dimension in a mean-field system of particles