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VOL. 57 | 2010 On Wasserstein geometry of Gaussian measures
Asuka Takatsu

Editor(s) Motoko Kotani, Masanori Hino, Takashi Kumagai

Abstract

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.

Information

Published: 1 January 2010
First available in Project Euclid: 24 November 2018

zbMATH: 1206.60016
MathSciNet: MR2648273

Digital Object Identifier: 10.2969/aspm/05710463

Subjects:
Primary: 28A33 , 60D05

Keywords: Gaussian measures , Wasserstein space

Rights: Copyright © 2010 Mathematical Society of Japan

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