Pré-Publication, Document De Travail Année : 2026

Concentration of the empirical measure in Wasserstein distance: bounds involving the covering dimension

Résumé

We give concentration inequalities in Wasserstein distance for the empirical measure of a sequence of independent and identically distributed random variables with values in a Polish space E. These inequalities involve the covering dimension of the support of the distribution of the variables. More precisely, we obtain a complete extension of the concentration inequalities of Fournier and Guillin [2015] in the case where E = R^d , in which the covering dimension replaces the dimension of the ambient space E.

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Dates et versions

hal-05460632 , version 1 (15-01-2026)

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Jérôme Dedecker, Aurélie Fischer, Bertrand Michel. Concentration of the empirical measure in Wasserstein distance: bounds involving the covering dimension. 2026. ⟨hal-05460632⟩
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