arXiv subjects

François Bolley

Publications and source records attributed to François Bolley.

20 records · Page 2Linked to original sources

arXiv2005

Quantitative concentration inequalities on sample path space for mean field interaction

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.

math.PR↗

arXiv2005

Concentration inequalities on product spaces with applications to Markov processes

For a stochastic process with state space some Polish space, this paper gives sufficient conditions on the initial and conditional distributions for the joint law to satisfy Gaussian concentration inequalities, transportation inequalities and also logarithmic Sobolev inequalities in the case of the Euclidean space. In several cases, the obtained constants are of optimal order of growth with respect to the number of variables, or are independent of this number. These results extend results known for mutually independent variables to weakly dependent variables under Dobrushin-Shlosman type conditions.

math.PR↗