Exponential rate of convergence independent of the dimension in a mean-field system of particles
Słowa kluczowe:Mean-field model, Poincaré inequality, transportation inequality, high dimension
EXPONENTIAL RATE OF CONVERGENCE INDEPENDENT OF THE DIMENSION IN A MEAN-FIELD SYSTEM OF PARTICLES
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.