Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- Probabilistic Approach to Geometry, M. Kotani, M. Hino and T. Kumagai, eds. (Tokyo: Mathematical Society of Japan, 2010), 463 - 472
On Wasserstein geometry of Gaussian measures
The space of Gaussian measures on a Euclidean space is geodesically convex in the $L^2$-Wasserstein space. This is a finite dimensional manifold since Gaussian measures are parameterized by means and covariance matrices. By restricting to the space of Gaussian measures inside the $L^2$-Wasserstein space, we manage to provide detailed descriptions of the $L^2$-Wasserstein geometry from a Riemannian geometric viewpoint. We obtain a formula for the sectional curvatures of the space of Gaussian measures, which is written out in terms of the eigenvalues of the covariance matrix.
Received: 15 January 2009
Revised: 1 May 2009
First available in Project Euclid: 24 November 2018
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Takatsu, Asuka. On Wasserstein geometry of Gaussian measures. Probabilistic Approach to Geometry, 463--472, Mathematical Society of Japan, Tokyo, Japan, 2010. doi:10.2969/aspm/05710463. https://projecteuclid.org/euclid.aspm/1543086332