On Wasserstein geometry of the space of Gaussian measures

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dc.creatorTakatsu, Asuka
dc.date2008-01-15
dc.date2009-02-11
dc.date.accessioned2026-07-07T12:39:40Z
dc.date.available2026-07-07T12:39:40Z
dc.descriptionThe space of Gaussian measures on a Euclidean space is geodesically convex in the $L^2$-Wasserstein space. This space 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 first construct a Riemannian metric which induces the $L^2$-Wasserstein distance. Then 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.
dc.description15pages, 1figures
dc.identifierhttps://arxiv.org/abs/0801.2250
dc.identifierhttp://arxiv.org/abs/0801.2250
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/219190
dc.subjectDifferential Geometry
dc.subjectProbability
dc.subject60D05; 28A33
dc.titleOn Wasserstein geometry of the space of Gaussian measures
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