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Contents of PMS, Vol. 37, Fasc. 1,
pages 145 - 161
 

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.

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