Wasserstein Geometry of Gaussian Measures
نویسنده
چکیده
This paper concerns the Riemannian/Alexandrov geometry of Gaussian measures, from the view point of the L2-Wasserstein geometry. The space of Gaussian measures is of finite dimension, which allows to write down the explicit Riemannian metric which in turn induces the L2-Wasserstein distance. Moreover, its completion as a metric space provides a complete picture of the singular behavior of the L2-Wasserstein geometry. In particular, the singular set is stratified according to the dimension of the support of the Gaussian measures, providing an explicit nontrivial example of Alexandrov space with extremal sets.
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