Convergence of the empirical measure in expected Wasserstein distance: non asymptotic explicit bounds in ℝ^d

09/02/2022

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by   Nicolas Fournier, et al.

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We provide some non asymptotic bounds, with explicit constants, that measure the rate of convergence, in expected Wasserstein distance, of the empirical measure associated to an i.i.d. N-sample of a given probability distribution on ℝ^d. We consider the cases where ℝ^d is endowed with the maximum and Euclidean norms.