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Quantitative concentration inequalities for empirical measures on non-compact spaces

Francois Bolley·Arnaud Guillin·Cedric Villani
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Abstract

We establish some 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 moments estimates for solutions of certain diffusive partial differential equations.

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Francois Bolley, Arnaud Guillin, Cedric Villani. 2005-03-07. Quantitative concentration inequalities for empirical measures on non-compact spaces. https://arxiv.org/abs/math/0503123

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