Quantitative concentration inequalities on sample path space for mean field interaction

François Bolley (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

We consider a system of particles experiencing diffusion and mean field interaction, and study its behaviour when the number of particles goes to infinity. We derive non-asymptotic large deviation bounds measuring the concentration of the empirical measure of the paths of the particles around its limit. The method is based on a coupling argument, strong integrability estimates on the paths in Holder norm, and some general concentration result for the empirical measure of identically distributed independent paths.

Mots clés: Mean fields limits; Sanov theorem; Transportation inequalities

Domaines: Probabilités [math.PR]

François Bolley. Quantitative concentration inequalities on sample path space for mean field interaction. 2005. ⟨hal-00014964⟩