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

Dyda B., Tugaut J.

Probability and Mathematical Statistics

2017

Vol. 37, Fasc. 1

145--161

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 Poincaré inequality. Then, we establish a so-called WJ-inequality, which is independent of the number of particles.