Approximation by finitely supported measures
Optimization and Control
2012-07-17 v3 Functional Analysis
Abstract
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.
Cite
@article{arxiv.1003.1035,
title = {Approximation by finitely supported measures},
author = {Benoit Kloeckner},
journal= {arXiv preprint arXiv:1003.1035},
year = {2012}
}
Comments
v2: the main result is extended to measures defined on a manifold. v3: references added. 25 pp. To appear in ESAIM:COCV