Accessibility navigation


Isometric study of Wasserstein spaces - the real line

Geher, G., Titkos, T. and Virosztek, D. (2020) Isometric study of Wasserstein spaces - the real line. Transactions of the American Mathematical Society. ISSN 1088-6850 (In Press)

[img] Text - Accepted Version
· Restricted to Repository staff only
· The Copyright of this document has not been checked yet. This may affect its availability.

505kB

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

Abstract/Summary

Recently Kloeckner described the structure of the isometry group of the quadratic Wasserstein space $\mathcal{W}_2(\R^n)$. It turned out that the case of the real line is exceptional in the sense that there exists an exotic isometry flow. Following this line of investigation, we compute $\isom\ler{\Wp(\R)}$, the isometry group of the Wasserstein space $\Wp(\R)$ for all $p \in [1, \infty)\setminus\{2\}$. We show that $\mathcal{W}_2(\R)$ is also exceptional regarding the parameter $p$: $\Wp(\R)$ is isometrically rigid if and only if $p\neq 2$. Regarding the underlying space, we prove that the exceptionality of $p=2$ disappears if we replace $\R$ by the compact interval $[0,1]$. Surprisingly, in that case, $\Wp\zo$ is isometrically rigid if and only if $p\neq1$. Moreover, $\Wo\zo$ admits isometries that split mass, and $\isom\ler{\Wo\zo}$ cannot be embedded into $\isom\ler{\wor}$.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:85689
Publisher:American Mathematical Society

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

Page navigation