Quantitative Concentration Inequalities for Empirical Measures on Non-compact Spaces |
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| Authors: | François Bolley Arnaud Guillin Cédric Villani |
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| Institution: | (1) ENS Lyon, Umpa, 46 allée d’Italie, F69364 Lyon Cedex 07, France;(2) Present address: CEREMADE, Université Paris Dauphine, Paris, France;(3) Institut de mathématiques, LSP, Université Paul Sabatier, F31062 Toulouse cedex 9, France |
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| Abstract: | 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. |
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| Keywords: | Transport inequalities Sanov Theorem |
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