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arXiv · 1412.4026

Asymptotic quantization for probability measures on Riemannian manifolds

Mikaela Iacobelli
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Abstract

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 $\mathbb{R}^d.$ 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.

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Mikaela Iacobelli. 2014-12-12. Asymptotic quantization for probability measures on Riemannian manifolds. https://arxiv.org/abs/1412.4026

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