---
_id: '6843'
abstract:
- lang: eng
  text: 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<∞.
article_number: '123435'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: György Pál
  full_name: Gehér, György Pál
  last_name: Gehér
- first_name: Tamás
  full_name: Titkos, Tamás
  last_name: Titkos
- first_name: Daniel
  full_name: Virosztek, Daniel
  id: 48DB45DA-F248-11E8-B48F-1D18A9856A87
  last_name: Virosztek
  orcid: 0000-0003-1109-5511
citation:
  ama: Gehér GP, Titkos T, Virosztek D. On isometric embeddings of Wasserstein spaces
    – the discrete case. <i>Journal of Mathematical Analysis and Applications</i>.
    2019;480(2). doi:<a href="https://doi.org/10.1016/j.jmaa.2019.123435">10.1016/j.jmaa.2019.123435</a>
  apa: Gehér, G. P., Titkos, T., &#38; Virosztek, D. (2019). On isometric embeddings
    of Wasserstein spaces – the discrete case. <i>Journal of Mathematical Analysis
    and Applications</i>. Elsevier. <a href="https://doi.org/10.1016/j.jmaa.2019.123435">https://doi.org/10.1016/j.jmaa.2019.123435</a>
  chicago: Gehér, György Pál, Tamás Titkos, and Daniel Virosztek. “On Isometric Embeddings
    of Wasserstein Spaces – the Discrete Case.” <i>Journal of Mathematical Analysis
    and Applications</i>. Elsevier, 2019. <a href="https://doi.org/10.1016/j.jmaa.2019.123435">https://doi.org/10.1016/j.jmaa.2019.123435</a>.
  ieee: G. P. Gehér, T. Titkos, and D. Virosztek, “On isometric embeddings of Wasserstein
    spaces – the discrete case,” <i>Journal of Mathematical Analysis and Applications</i>,
    vol. 480, no. 2. Elsevier, 2019.
  ista: Gehér GP, Titkos T, Virosztek D. 2019. On isometric embeddings of Wasserstein
    spaces – the discrete case. Journal of Mathematical Analysis and Applications.
    480(2), 123435.
  mla: Gehér, György Pál, et al. “On Isometric Embeddings of Wasserstein Spaces –
    the Discrete Case.” <i>Journal of Mathematical Analysis and Applications</i>,
    vol. 480, no. 2, 123435, Elsevier, 2019, doi:<a href="https://doi.org/10.1016/j.jmaa.2019.123435">10.1016/j.jmaa.2019.123435</a>.
  short: G.P. Gehér, T. Titkos, D. Virosztek, Journal of Mathematical Analysis and
    Applications 480 (2019).
date_created: 2019-09-01T22:01:01Z
date_published: 2019-12-15T00:00:00Z
date_updated: 2025-07-10T11:53:55Z
day: '15'
department:
- _id: LaEr
doi: 10.1016/j.jmaa.2019.123435
ec_funded: 1
external_id:
  arxiv:
  - '1809.01101'
  isi:
  - '000486563900031'
intvolume: '       480'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1809.01101
month: '12'
oa: 1
oa_version: Preprint
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '291734'
  name: International IST Postdoc Fellowship Programme
publication: Journal of Mathematical Analysis and Applications
publication_identifier:
  eissn:
  - 1096-0813
  issn:
  - 0022-247X
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: On isometric embeddings of Wasserstein spaces – the discrete case
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 480
year: '2019'
...