---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '21018'
abstract:
- lang: eng
  text: In this paper, we review recent results on stability and instability in logarithmic
    Sobolev inequalities, with a particular emphasis on strong norms. We consider
    several versions of these inequalities on the Euclidean space, for the Lebesgue
    and the Gaussian measures, and discuss their differences in terms of moments and
    stability. We give new and direct proofs, as well as examples and discuss the
    stability of a logarithmic uncertainty principle. Although we do not cover all
    aspects of the topic, we hope to contribute to establishing the state of the art.
acknowledgement: This work has been supported by the Project Conviviality (ANR-23-CE40–0003)
  of the French National Research Agency. G.B. has received funding from the European
  Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie
  grant agreement No 101034413. The authors thank a referee for a careful reading
  and suggestions which result in a significant improvement of the manuscript. Open
  access funding provided by Institute of Science and Technology (IST Austria). The
  work of GB has received funding from the European Union’s Horizon 2020 research
  and innovation programme under the Marie Skłodowska-Curie grant agreement No 101034413.
  This work has been supported by the Project Conviviality (ANR-23-CE40–0003) of the
  French National Research Agency.
article_number: '5'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Giovanni
  full_name: Brigati, Giovanni
  id: 63ff57e8-1fbb-11ee-88f2-f558ffc59cf1
  last_name: Brigati
- first_name: Jean
  full_name: Dolbeault, Jean
  last_name: Dolbeault
- first_name: Nikita
  full_name: Simonov, Nikita
  last_name: Simonov
citation:
  ama: 'Brigati G, Dolbeault J, Simonov N. Logarithmic Sobolev Inequalities: A review
    on stability and instability results. <i>La Matematica</i>. 2026;5. doi:<a href="https://doi.org/10.1007/s44007-025-00180-y">10.1007/s44007-025-00180-y</a>'
  apa: 'Brigati, G., Dolbeault, J., &#38; Simonov, N. (2026). Logarithmic Sobolev
    Inequalities: A review on stability and instability results. <i>La Matematica</i>.
    Springer Nature. <a href="https://doi.org/10.1007/s44007-025-00180-y">https://doi.org/10.1007/s44007-025-00180-y</a>'
  chicago: 'Brigati, Giovanni, Jean Dolbeault, and Nikita Simonov. “Logarithmic Sobolev
    Inequalities: A Review on Stability and Instability Results.” <i>La Matematica</i>.
    Springer Nature, 2026. <a href="https://doi.org/10.1007/s44007-025-00180-y">https://doi.org/10.1007/s44007-025-00180-y</a>.'
  ieee: 'G. Brigati, J. Dolbeault, and N. Simonov, “Logarithmic Sobolev Inequalities:
    A review on stability and instability results,” <i>La Matematica</i>, vol. 5.
    Springer Nature, 2026.'
  ista: 'Brigati G, Dolbeault J, Simonov N. 2026. Logarithmic Sobolev Inequalities:
    A review on stability and instability results. La Matematica. 5, 5.'
  mla: 'Brigati, Giovanni, et al. “Logarithmic Sobolev Inequalities: A Review on Stability
    and Instability Results.” <i>La Matematica</i>, vol. 5, 5, Springer Nature, 2026,
    doi:<a href="https://doi.org/10.1007/s44007-025-00180-y">10.1007/s44007-025-00180-y</a>.'
  short: G. Brigati, J. Dolbeault, N. Simonov, La Matematica 5 (2026).
corr_author: '1'
date_created: 2026-01-20T10:14:55Z
date_published: 2026-01-08T00:00:00Z
date_updated: 2026-01-21T07:48:28Z
day: '08'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s44007-025-00180-y
ec_funded: 1
external_id:
  arxiv:
  - '2504.08658'
file:
- access_level: open_access
  checksum: 0702d8397f216555b1d5286e5d77f09c
  content_type: application/pdf
  creator: dernst
  date_created: 2026-01-21T07:45:03Z
  date_updated: 2026-01-21T07:45:03Z
  file_id: '21025'
  file_name: 2026_LaMatematica_Brigati.pdf
  file_size: 4992025
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file_date_updated: 2026-01-21T07:45:03Z
has_accepted_license: '1'
intvolume: '         5'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
  call_identifier: H2020
  grant_number: '101034413'
  name: 'IST-BRIDGE: International postdoctoral program'
publication: La Matematica
publication_identifier:
  issn:
  - 2730-9657
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Logarithmic Sobolev Inequalities: A review on stability and instability results'
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 5
year: '2026'
...