Cone structure of $L^2$-Wasserstein spaces
Cone structure of $L^2$-Wasserstein spaces
复制标题
$L^2$-Wasserstein 空间的锥体结构
DOI：
10.1142/s1793525312500112
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发表时间：
2012
影响因子：
0.8
通讯作者：
Takumi YOKOTA
中科院分区：
文献类型：
--
作者：
Asuka TAKATSU;Takumi YOKOTA
本文的目的是更好地理解可分Hilbert空间上的二次Wasserstein空间的几何结构。为此，我们专注于他们的锥和产品的结构，并证明了二次Wasserstein空间在任何可分的Hilbert空间有一个锥结构和等距分裂的基础空间，但不超过。这些都显示在更一般的设置，我们的主要结果之一是，二次Wasserstein空间在波兰空间有一个锥结构，当且仅当这样做的基础空间。
The aim of this paper is to obtain a better understanding of the geometric structure of quadratic Wasserstein spaces over separable Hilbert spaces. For this sake, we focus on their cone and product structures, and prove that the quadratic Wasserstein space over any separable Hilbert space has a cone structure and splits the underlying space isometrically but no more than that. These are shown in more general settings, and one of our main results is that the quadratic Wasserstein space over a Polish space has a cone structure if and only if so does the underlying space.