---
_id: '7389'
abstract:
- lang: eng
  text: "Recently Kloeckner described the structure of the isometry group of the quadratic
    Wasserstein space 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(W_p(R)), the isometry group of the Wasserstein
    space\r\nW_p(R) for all p \\in [1,\\infty) \\setminus {2}. We show that W_2(R)
    is also exceptional regarding the\r\nparameter p: W_p(R) is isometrically rigid
    if and only if p is not equal to 2. Regarding the underlying\r\nspace, we prove
    that the exceptionality of p = 2 disappears if we replace R by the compact\r\ninterval
    [0,1]. Surprisingly, in that case, W_p([0,1]) is isometrically rigid if and only
    if\r\np is not equal to 1. Moreover, W_1([0,1]) admits isometries that split mass,
    and Isom(W_1([0,1]))\r\ncannot be embedded into Isom(W_1(R))."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Gyorgy Pal
  full_name: Geher, Gyorgy Pal
  last_name: Geher
- first_name: Tamas
  full_name: Titkos, Tamas
  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: Geher GP, Titkos T, Virosztek D. Isometric study of Wasserstein spaces - the
    real line. <i>Transactions of the American Mathematical Society</i>. 2020;373(8):5855-5883.
    doi:<a href="https://doi.org/10.1090/tran/8113">10.1090/tran/8113</a>
  apa: Geher, G. P., Titkos, T., &#38; Virosztek, D. (2020). Isometric study of Wasserstein
    spaces - the real line. <i>Transactions of the American Mathematical Society</i>.
    American Mathematical Society. <a href="https://doi.org/10.1090/tran/8113">https://doi.org/10.1090/tran/8113</a>
  chicago: Geher, Gyorgy Pal, Tamas Titkos, and Daniel Virosztek. “Isometric Study
    of Wasserstein Spaces - the Real Line.” <i>Transactions of the American Mathematical
    Society</i>. American Mathematical Society, 2020. <a href="https://doi.org/10.1090/tran/8113">https://doi.org/10.1090/tran/8113</a>.
  ieee: G. P. Geher, T. Titkos, and D. Virosztek, “Isometric study of Wasserstein
    spaces - the real line,” <i>Transactions of the American Mathematical Society</i>,
    vol. 373, no. 8. American Mathematical Society, pp. 5855–5883, 2020.
  ista: Geher GP, Titkos T, Virosztek D. 2020. Isometric study of Wasserstein spaces
    - the real line. Transactions of the American Mathematical Society. 373(8), 5855–5883.
  mla: Geher, Gyorgy Pal, et al. “Isometric Study of Wasserstein Spaces - the Real
    Line.” <i>Transactions of the American Mathematical Society</i>, vol. 373, no.
    8, American Mathematical Society, 2020, pp. 5855–83, doi:<a href="https://doi.org/10.1090/tran/8113">10.1090/tran/8113</a>.
  short: G.P. Geher, T. Titkos, D. Virosztek, Transactions of the American Mathematical
    Society 373 (2020) 5855–5883.
date_created: 2020-01-29T10:20:46Z
date_published: 2020-08-01T00:00:00Z
date_updated: 2023-08-17T14:31:03Z
day: '01'
ddc:
- '515'
department:
- _id: LaEr
doi: 10.1090/tran/8113
ec_funded: 1
external_id:
  arxiv:
  - '2002.00859'
  isi:
  - '000551418100018'
intvolume: '       373'
isi: 1
issue: '8'
keyword:
- Wasserstein space
- isometric embeddings
- isometric rigidity
- exotic isometry flow
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2002.00859
month: '08'
oa: 1
oa_version: Preprint
page: 5855-5883
project:
- _id: 26A455A6-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '846294'
  name: Geometric study of Wasserstein spaces and free probability
publication: Transactions of the American Mathematical Society
publication_identifier:
  eissn:
  - '10886850'
  issn:
  - '00029947'
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
status: public
title: Isometric study of Wasserstein spaces - the real line
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 373
year: '2020'
...