EXPONENTIAL RATE OF CONVERGENCE INDEPENDENT OF THE
DIMENSION IN A MEAN-FIELD SYSTEM OF PARTICLES

Bartłomiej Dyda

Julian Tugaut

Abstract: 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.

2010 AMS Mathematics Subject Classification: Primary: 60F10; Secondary: 60J60,
60G10.

Keywords and phrases: Mean-field model, Poincaré inequality, transportation
inequality, high dimension.