Benoit Kloeckner
Published 2010-03-04, updated 2010-12-03Version 3
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. This question has been studied under the names of ``quantization of distributions'' and, when p=1, ``location problem''. When p=2, it is linked with Centroidal Voronoi Tessellations.
Comments: v2: the main result is extended to measures defined on a manifold. v3: references added. 25 pp. To appear in ESAIM:COCV
Journal: ESAIM: Control, Optimisation and Calculus of Variations 18, 2 (2012) 343
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