Wasserstein geometry of Gaussian measures
Wasserstein geometry of Gaussian measures
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DOI：
10.18910/4973
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发表时间：
2011-12
影响因子：
0.4
通讯作者：
Asuka Takatsu
中科院分区：
文献类型：
--
作者：
Asuka Takatsu
本文从L2-Wasserstein几何的观点出发，研究了Gauss测度的Riemann/Alexandrov几何.高斯测度的空间是有限维的，这使得可以写出显式黎曼度量，这反过来又导致了L2-Wasserstein距离。此外，它作为度量空间的完备化提供了L2 Wasserstein几何奇异行为的完整图像。特别地，根据高斯测度的支撑维数确定了奇异集，给出了Alexandrov空间具有极值集的一个显式非平凡例子.
This paper concerns the Riemannian/Alexandrov geometry of Gaussian measures, from the view point of the L 2 -Wasserstein geometry. The space of Gaussian measures is of finite dimension, which allows to write down the ex plicit Riemannian metric which in turn induces the L 2 -Wasserstein distance. Moreover, its completion as a metric space provides a complete picture of the singular behavior of the L 2 Wasserstein geometry. In particular, the singular set is st ratified according to the dimension of the support of the Gaussian measures, providing an explicit nontrivial example of Alexandrov space with extremal sets.