Quantitative concentration inequalities on sample path space for mean field interaction

François Bolley

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Quantitative concentration inequalities on sample path space for mean field interaction

François Bolley

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Abstract

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.

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François Bolley. 2005-11-30. Quantitative concentration inequalities on sample path space for mean field interaction. https://arxiv.org/abs/math/0511752

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