Asymptotic quantization for probability measures on Riemannian manifolds
Asymptotic quantization for probability measures on Riemannian manifolds
复制标题
黎曼流形上概率测度的渐近量化
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Mikaela Iacobelli
中科院分区：
文献类型：
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作者：
Mikaela Iacobelli
本文研究黎曼流形上概率测度的量子化问题。在一个关于测度在无穷远处增长的适当假设下，我们得到了量化误差的渐近估计，推广了RD的结果。我们的增长假设依赖于流形的曲率，并且在平坦的情况下，简化为矩条件。我们还建立了一个例子，表明我们的假设是尖锐的。
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.