---
_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'
...
---
_id: '175'
abstract:
- lang: eng
  text: An upper bound sieve for rational points on suitable varieties isdeveloped,
    together with applications tocounting rational points in thin sets,to local solubility
    in families, and to the notion of “friable” rational pointswith respect to divisors.
    In the special case of quadrics, sharper estimates areobtained by developing a
    version of the Selberg sieve for rational points.
article_processing_charge: No
arxiv: 1
author:
- first_name: Timothy D
  full_name: Browning, Timothy D
  id: 35827D50-F248-11E8-B48F-1D18A9856A87
  last_name: Browning
  orcid: 0000-0002-8314-0177
- first_name: Daniel
  full_name: Loughran, Daniel
  last_name: Loughran
citation:
  ama: Browning TD, Loughran D. Sieving rational points on varieties. <i>Transactions
    of the American Mathematical Society</i>. 2019;371(8):5757-5785. doi:<a href="https://doi.org/10.1090/tran/7514">10.1090/tran/7514</a>
  apa: Browning, T. D., &#38; Loughran, D. (2019). Sieving rational points on varieties.
    <i>Transactions of the American Mathematical Society</i>. American Mathematical
    Society. <a href="https://doi.org/10.1090/tran/7514">https://doi.org/10.1090/tran/7514</a>
  chicago: Browning, Timothy D, and Daniel Loughran. “Sieving Rational Points on Varieties.”
    <i>Transactions of the American Mathematical Society</i>. American Mathematical
    Society, 2019. <a href="https://doi.org/10.1090/tran/7514">https://doi.org/10.1090/tran/7514</a>.
  ieee: T. D. Browning and D. Loughran, “Sieving rational points on varieties,” <i>Transactions
    of the American Mathematical Society</i>, vol. 371, no. 8. American Mathematical
    Society, pp. 5757–5785, 2019.
  ista: Browning TD, Loughran D. 2019. Sieving rational points on varieties. Transactions
    of the American Mathematical Society. 371(8), 5757–5785.
  mla: Browning, Timothy D., and Daniel Loughran. “Sieving Rational Points on Varieties.”
    <i>Transactions of the American Mathematical Society</i>, vol. 371, no. 8, American
    Mathematical Society, 2019, pp. 5757–85, doi:<a href="https://doi.org/10.1090/tran/7514">10.1090/tran/7514</a>.
  short: T.D. Browning, D. Loughran, Transactions of the American Mathematical Society
    371 (2019) 5757–5785.
date_created: 2018-12-11T11:45:01Z
date_published: 2019-04-15T00:00:00Z
date_updated: 2023-08-24T14:34:56Z
day: '15'
department:
- _id: TiBr
doi: 10.1090/tran/7514
external_id:
  arxiv:
  - '1705.01999'
  isi:
  - '000464034200019'
intvolume: '       371'
isi: 1
issue: '8'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1705.01999
month: '04'
oa: 1
oa_version: Preprint
page: 5757-5785
publication: Transactions of the American Mathematical Society
publication_identifier:
  eissn:
  - '10886850'
  issn:
  - '00029947'
publication_status: published
publisher: American Mathematical Society
publist_id: '7746'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Sieving rational points on varieties
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 371
year: '2019'
...