We consider the problem of approximating a probability measure defined on a metric space by a measure supported on a finite number of points. More specifically we seek the asymptotic behavior of the minimal Wasserstein distance to an approximation when the number of points goes to infinity. The main result gives an equivalent when the space is a Riemannian manifold and the approximated measure is absolutely continuous and compactly supported.
Mots clés : measures, Wasserstein distance, quantization, location problem, centroidal Voronoi tessellations
@article{COCV_2012__18_2_343_0,
author = {Kloeckner, Beno{\^\i}t},
title = {Approximation by finitely supported measures},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {343--359},
publisher = {EDP-Sciences},
volume = {18},
number = {2},
year = {2012},
doi = {10.1051/cocv/2010100},
mrnumber = {2954629},
zbl = {1246.49040},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv/2010100/}
}
TY - JOUR AU - Kloeckner, Benoît TI - Approximation by finitely supported measures JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2012 SP - 343 EP - 359 VL - 18 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2010100/ DO - 10.1051/cocv/2010100 LA - en ID - COCV_2012__18_2_343_0 ER -
%0 Journal Article %A Kloeckner, Benoît %T Approximation by finitely supported measures %J ESAIM: Control, Optimisation and Calculus of Variations %D 2012 %P 343-359 %V 18 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2010100/ %R 10.1051/cocv/2010100 %G en %F COCV_2012__18_2_343_0
Kloeckner, Benoît. Approximation by finitely supported measures. ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 2, pp. 343-359. doi : 10.1051/cocv/2010100. http://archive.numdam.org/articles/10.1051/cocv/2010100/
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