Quantitative concentration inequalities for empirical measures on non compact spaces

Bolley, François; Guillin, Arnaud; Villani, Cédric

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

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Type

Article accepté pour publication ou publié

Date

2007

Journal name

Probability Theory and Related Fields

Volume

137

Number

3-4

Publisher

Springer

Pages

541-593

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 / Keywords

Transport inequalities; Sanov Theorem