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

Bartłomiej Dyda (1) , Julian Tugaut (2)

1 IMCS - Institute of Mathematics and Computer Science [Wroclaw]
2 PSPM - Probabilités, statistique, physique mathématique

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 from the number of particles.

Domaines: Probabilités [math.PR]

Bartłomiej Dyda, Julian Tugaut. Exponential rate of convergence independent from the dimension in a mean-field system of particles. Probability and Mathematical Statistics, 2017. ⟨hal-01119526⟩