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A short proof on the rate of convergence of the empirical measure for the Wasserstein distance

01/20/2021

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by Vincent Divol, et al.

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We provide a short proof that the Wasserstein distance between the empirical measure of a n-sample and the estimated measure is of order n^-(1/d), if the measure has a lower and upper bounded density on the d-dimensional flat torus.

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