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

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Abstract

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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Dates and versions

hal-03117283 , version 1 (21-01-2021)

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  • HAL Id : hal-03117283 , version 1

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Vincent Divol. A short proof on the rate of convergence of the empirical measure for the Wasserstein distance. 2021. ⟨hal-03117283⟩
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