On isometric embeddings of Wasserstein spaces – the discrete case

G.P. Gehér, T. Titkos, D. Virosztek, Journal of Mathematical Analysis and Applications 480 (n.d.).


Journal Article | In Press | English
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Abstract
The aim of this short paper is to offer a complete characterization of all (not necessarily surjective) isometric embeddings of the Wasserstein space Wp(X), where S is a countable discrete metric space and 0<p<∞ is any parameter value. Roughly speaking, we will prove that any isometric embedding can be described by a special kind of X×(0,1]-indexed family of nonnegative finite measures. Our result implies that a typical non-surjective isometric embedding of Wp(X) 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 Wp(X) is isometrically rigid for all 0<p<∞.
Publishing Year
Date Published
2019-09-04
Journal Title
Journal of Mathematical Analysis and Applications
Volume
480
Issue
2
Article Number
123435
ISSN
eISSN
IST-REx-ID

Cite this

Gehér GP, Titkos T, Virosztek D. On isometric embeddings of Wasserstein spaces – the discrete case. Journal of Mathematical Analysis and Applications. 480(2). doi:10.1016/j.jmaa.2019.123435
Gehér, G. P., Titkos, T., & Virosztek, D. (n.d.). On isometric embeddings of Wasserstein spaces – the discrete case. Journal of Mathematical Analysis and Applications, 480(2). https://doi.org/10.1016/j.jmaa.2019.123435
Gehér, György Pál, Tamás Titkos, and Daniel Virosztek. “On Isometric Embeddings of Wasserstein Spaces – the Discrete Case.” Journal of Mathematical Analysis and Applications 480, no. 2 (n.d.). https://doi.org/10.1016/j.jmaa.2019.123435.
G. P. Gehér, T. Titkos, and D. Virosztek, “On isometric embeddings of Wasserstein spaces – the discrete case,” Journal of Mathematical Analysis and Applications, vol. 480, no. 2.
Gehér GP, Titkos T, Virosztek D. On isometric embeddings of Wasserstein spaces – the discrete case. Journal of Mathematical Analysis and Applications. 480(2).
Gehér, György Pál, et al. “On Isometric Embeddings of Wasserstein Spaces – the Discrete Case.” Journal of Mathematical Analysis and Applications, vol. 480, no. 2, 123435, Elsevier, doi:10.1016/j.jmaa.2019.123435.

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