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

Vincent Divol 1, 2
2 DATASHAPE - Understanding the Shape of Data
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
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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https://hal.inria.fr/hal-03117283
Contributor : Vincent Divol Connect in order to contact the contributor
Submitted on : Thursday, January 21, 2021 - 9:33:22 AM
Last modification on : Monday, December 13, 2021 - 9:16:38 AM
Long-term archiving on: : Thursday, April 22, 2021 - 6:17:06 PM

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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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