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Fournier, Nicolas; Guillin, Arnaud
Probability theory and related fields, 08/2015, Letnik: 162, Številka: 3-4Journal Article
Let μ N be the empirical measure associated to a N -sample of a given probability distribution μ on R d . We are interested in the rate of convergence of μ N to μ , when measured in the Wasserstein distance of order p > 0 . We provide some satisfying non-asymptotic L p -bounds and concentration inequalities, for any values of p > 0 and d ≥ 1 . We extend also the non asymptotic L p -bounds to stationary ρ -mixing sequences, Markov chains, and to some interacting particle systems.
