Quantitative concentration inequalities for empirical measures on   non-compact spaces
  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. 
Francois Bolley, Arnaud Guillin, Cedric Villani