Convergence of the empirical measure in expected Wasserstein distance: non asymptotic explicit bounds in $\mathbb{R}^d$

Nicolas Fournier

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Convergence of the empirical measure in expected Wasserstein distance: non asymptotic explicit bounds in $\mathbb{R}^d$

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arxiv 2209.00923 v2 pith:BYRD3P57 submitted 2022-09-02 math.PR math.STstat.TH

Nicolas Fournier This is my paper · ORCID

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keywords measureasymptoticboundsconvergencedistanceempiricalexpectedexplicit

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abstract

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 $\mathbb{R}^d$.

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