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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Bolley, F., Guillin, A. & Villani, C. Quantitative Concentration Inequalities for Empirical Measures on Non-compact Spaces. Probab. Theory Relat. Fields 137, 541–593 (2007). https://doi.org/10.1007/s00440-006-0004-7
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DOI: https://doi.org/10.1007/s00440-006-0004-7