Asymptotic quantization for probability measures on Riemannian manifolds
Iacobelli, Mikaela1, 2
1 University of Rome Sapienza, Department of Mathematics Guido Castelnuovo, Piazzale Aldo Moro 5, 00185 Rome, Italy.
2 Ecole Polytechnique, Centre de mathématiques Laurent Schwartz, 91128 Palaiseau cedex, France.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 3, pp. 770-785.

In this paper we study the quantization problem for probability measures on Riemannian manifolds. Under a suitable assumption on the growth at infinity of the measure we find asymptotic estimates for the quantization error, generalizing the results on R d . Our growth assumption depends on the curvature of the manifold and reduces, in the flat case, to a moment condition. We also build an example showing that our hypothesis is sharp.

Reçu le :
DOI : 10.1051/cocv/2015025
Classification : 49Q20
Mots-clés : Quantization of measures, Riemannian manifolds
Iacobelli, Mikaela 1, 2

1 University of Rome Sapienza, Department of Mathematics Guido Castelnuovo, Piazzale Aldo Moro 5, 00185 Rome, Italy.
2 Ecole Polytechnique, Centre de mathématiques Laurent Schwartz, 91128 Palaiseau cedex, France. 
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     title = {Asymptotic quantization for probability measures on {Riemannian} manifolds},
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     publisher = {EDP-Sciences},
     volume = {22},
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Iacobelli, Mikaela. Asymptotic quantization for probability measures on Riemannian manifolds. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 3, pp. 770-785. doi : 10.1051/cocv/2015025. http://www.numdam.org/articles/10.1051/cocv/2015025/

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