Approximation by finitely supported measures
Résumé
Given a compactly supported probability measure on a Riemannian manifold, we study the asymptotic speed at which it can be approximated (in Wasserstein distance of any exponent p) by finitely supported measure. When p=1, this is the location problem and precise asymptotics where given by Bouchitté, Jimenez and Rajesh. When p=2, this problem is linked with Centroidal Voronoi Tessellations.
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