Open Access
Translator Disclaimer
December 2011 Wasserstein geometry of Gaussian measures
Asuka Takatsu
Osaka J. Math. 48(4): 1005-1026 (December 2011).

Abstract

This paper concerns the Riemannian/Alexandrov geometry of Gaussian measures, from the view point of the $L^{2}$-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 $L^{2}$-Wasserstein distance. Moreover, its completion as a metric space provides a complete picture of the singular behavior of the $L^{2}$-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.

Citation

Download Citation

Asuka Takatsu. "Wasserstein geometry of Gaussian measures." Osaka J. Math. 48 (4) 1005 - 1026, December 2011.

Information

Published: December 2011
First available in Project Euclid: 11 January 2012

zbMATH: 1245.60013
MathSciNet: MR2648273

Subjects:
Primary: 53C23 , 60D05

Rights: Copyright © 2011 Osaka University and Osaka City University, Departments of Mathematics

JOURNAL ARTICLE
22 PAGES


SHARE
Vol.48 • No. 4 • December 2011
Back to Top