Approximation by finitely supported measures

Benoit Kloeckner (1)

1 IF - Institut Fourier

Given a compactly supported probability measure on Euclidean space, 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.

Mots clés: centroidal Voronoi tessellations.; centroidal Voronoi tessellations; Optimal transportation; location problem

Domaines: Optimisation et contrôle [math.OC]; Analyse fonctionnelle [math.FA]

Benoit Kloeckner. Approximation by finitely supported measures. 2010. ⟨hal-00461329v1⟩