Quantitative concentration inequalities for empirical measures on non compact spaces
Bolley, François; Guillin, Arnaud; Villani, Cédric (2007), Quantitative concentration inequalities for empirical measures on non compact spaces, Probability Theory and Related Fields, 137, 3-4, p. 541-593. http://dx.doi.org/10.1007/s00440-006-0004-7
TypeArticle accepté pour publication ou publié
Journal nameProbability Theory and Related Fields
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Abstract (EN)We establish quantitative concentration estimates for the empirical measure of many independent variables, in transportation distances. As an application, we provide some error bounds for particle simulations in a model mean field problem. The tools include coupling arguments, as well as regularity and moment estimates for solutions of certain diffusive partial differential equations.
Subjects / KeywordsTransport inequalities; Sanov Theorem
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