Accessibility navigation


On isometric embeddings of Wasserstein spaces - the discrete case

Geher, G. P., Titkos, T. and Virosztek, D. (2019) On isometric embeddings of Wasserstein spaces - the discrete case. Journal of Mathematical Analysis and Applications, 480 (2). 123435. ISSN 0022-247X

[img]
Preview
Text - Accepted Version
· Available under License Creative Commons Attribution Non-commercial No Derivatives.
· Please see our End User Agreement before downloading.

348kB

It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing.

To link to this item DOI: 10.1016/j.jmaa.2019.123435

Abstract/Summary

The aim of this short paper is to offer a complete characterization of all (not necessarily surjective) isometric embeddings of the Wasserstein space $\mathcal{W}_p(\X)$, where $\X$ is a countable discrete metric space and $0<p<\infty$ is any parameter value. Roughly speaking, we will prove that any isometric embedding can be described by a special kind of $\X\times(0,1]$-indexed family of nonnegative finite measures. Our result implies that a typical non-surjective isometric embedding of $\ws$ splits mass and does not preserve the shape of measures. In order to stress that the lack of surjectivity is what makes things challenging, we will prove alternatively that $\ws$ is isometrically rigid for all $0<p<\infty$.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:85683
Publisher:Elsevier

Downloads

Downloads per month over past year

University Staff: Request a correction | Centaur Editors: Update this record

Page navigation