Quantitative concentration inequalities on sample path space for mean field interaction

Details Quantitative concentration inequalities on sample path space for mean field interaction Quantitative concentration inequalities on sample path space for mean field interaction

2005-11-30

arxiv.org/abs/math/0511752v1

Mathematics

Probability

Scientific paper

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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