<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-04042046v1</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-24T15:33:29+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Stability for the logarithmic Sobolev inequality</title>
            <author role="aut">
              <persName>
                <forename type="first">Giovanni</forename>
                <surname>Brigati</surname>
              </persName>
              <email type="md5">adf8391a2f6504dc10d190f5fcd86ef1</email>
              <email type="domain">ceremade.dauphine.fr</email>
              <idno type="idhal" notation="string">giovanni-brigati</idno>
              <idno type="idhal" notation="numeric">1476236</idno>
              <idno type="halauthorid" notation="string">2655108-1476236</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-3698-9995</idno>
              <idno type="ARXIV">https://arxiv.org/a/brigati_g_1</idno>
              <affiliation ref="#struct-60"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Jean</forename>
                <surname>Dolbeault</surname>
              </persName>
              <email type="md5">3369e41b8636cf57d4d79bbdd1be8c8d</email>
              <email type="domain">ceremade.dauphine.fr</email>
              <idno type="idhal" notation="string">dolbeaul</idno>
              <idno type="idhal" notation="numeric">87</idno>
              <idno type="halauthorid" notation="string">570-87</idno>
              <idno type="RESEARCHERID">http://www.researcherid.com/rid/O-2328-2017</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-4234-2298</idno>
              <idno type="IDREF">https://www.idref.fr/120112507</idno>
              <idno type="RESEARCHERID">http://www.researcherid.com/rid/http://www.researcherid.com/rid/O-2328-2017</idno>
              <idno type="ARXIV">https://arxiv.org/a/dolbeault_j_1</idno>
              <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?user=ky2LFVsAAAAJ</idno>
              <affiliation ref="#struct-60"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Nikita</forename>
                <surname>Simonov</surname>
              </persName>
              <email type="md5">32bd665b8e9a0bc28da10cbf14121d23</email>
              <email type="domain">sorbonne-universite.fr</email>
              <idno type="idhal" notation="numeric">1216986</idno>
              <idno type="halauthorid" notation="string">1994923-1216986</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-3241-190X</idno>
              <affiliation ref="#struct-1005052"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Jean</forename>
                <surname>Dolbeault</surname>
              </persName>
              <email type="md5">3369e41b8636cf57d4d79bbdd1be8c8d</email>
              <email type="domain">ceremade.dauphine.fr</email>
            </editor>
            <funder>Marie Sklodowska-Curie grant agreement No 754362</funder>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2023-03-22 22:43:17</date>
              <date type="whenModified">2025-10-14 07:40:20</date>
              <date type="whenReleased">2023-03-27 12:14:54</date>
              <date type="whenProduced">2023-03-22</date>
              <date type="whenEndEmbargoed">2023-03-22</date>
              <ref type="file" target="https://hal.science/hal-04042046v1/document">
                <date notBefore="2023-03-22"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-04042046v1/file/BDS2023-LSI.pdf" id="file-4042046-3518242">
                <date notBefore="2023-03-22"/>
              </ref>
            </edition>
            <edition n="v2">
              <date type="whenSubmitted">2024-03-29 22:36:48</date>
            </edition>
            <edition n="v3">
              <date type="whenSubmitted">2024-07-10 17:03:08</date>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="101536">
                <persName>
                  <forename>Jean</forename>
                  <surname>Dolbeault</surname>
                </persName>
                <email type="md5">3369e41b8636cf57d4d79bbdd1be8c8d</email>
                <email type="domain">ceremade.dauphine.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-04042046</idno>
            <idno type="halUri">https://hal.science/hal-04042046</idno>
            <idno type="halBibtex">brigati:hal-04042046</idno>
            <idno type="halRefHtml">2023</idno>
            <idno type="halRef">2023</idno>
            <availability status="restricted">
              <licence target="https://creativecommons.org/licenses/by-nc/4.0/">CC BY-NC 4.0 - Attribution - Non-commercial use<ref corresp="#file-4042046-3518242"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt/>
          <notesStmt/>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Stability for the logarithmic Sobolev inequality</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Giovanni</forename>
                    <surname>Brigati</surname>
                  </persName>
                  <email type="md5">adf8391a2f6504dc10d190f5fcd86ef1</email>
                  <email type="domain">ceremade.dauphine.fr</email>
                  <idno type="idhal" notation="string">giovanni-brigati</idno>
                  <idno type="idhal" notation="numeric">1476236</idno>
                  <idno type="halauthorid" notation="string">2655108-1476236</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-3698-9995</idno>
                  <idno type="ARXIV">https://arxiv.org/a/brigati_g_1</idno>
                  <affiliation ref="#struct-60"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Jean</forename>
                    <surname>Dolbeault</surname>
                  </persName>
                  <email type="md5">3369e41b8636cf57d4d79bbdd1be8c8d</email>
                  <email type="domain">ceremade.dauphine.fr</email>
                  <idno type="idhal" notation="string">dolbeaul</idno>
                  <idno type="idhal" notation="numeric">87</idno>
                  <idno type="halauthorid" notation="string">570-87</idno>
                  <idno type="RESEARCHERID">http://www.researcherid.com/rid/O-2328-2017</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-4234-2298</idno>
                  <idno type="IDREF">https://www.idref.fr/120112507</idno>
                  <idno type="RESEARCHERID">http://www.researcherid.com/rid/http://www.researcherid.com/rid/O-2328-2017</idno>
                  <idno type="ARXIV">https://arxiv.org/a/dolbeault_j_1</idno>
                  <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?user=ky2LFVsAAAAJ</idno>
                  <affiliation ref="#struct-60"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Nikita</forename>
                    <surname>Simonov</surname>
                  </persName>
                  <email type="md5">32bd665b8e9a0bc28da10cbf14121d23</email>
                  <email type="domain">sorbonne-universite.fr</email>
                  <idno type="idhal" notation="numeric">1216986</idno>
                  <idno type="halauthorid" notation="string">1994923-1216986</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-3241-190X</idno>
                  <affiliation ref="#struct-1005052"/>
                </author>
              </analytic>
              <monogr>
                <imprint>
                  <date type="datePub">2023-03-22</date>
                </imprint>
              </monogr>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Logarithmic Sobolev inequality</term>
                <term xml:lang="en">stability</term>
                <term xml:lang="en">log-concavity</term>
                <term xml:lang="en">heat flow</term>
                <term xml:lang="en">entropy</term>
                <term xml:lang="en">carré du champ</term>
              </keywords>
              <classCode scheme="classification">39B62, 47J20, 49J40, 35A23, 35K85</classCode>
              <classCode scheme="halDomain" n="math">Mathematics [math]</classCode>
              <classCode scheme="halTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halOldTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halTreeTypology" n="UNDEFINED.PREPRINT">Preprints, Working Papers, ... - Preprint</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>This paper is devoted to stability results for the Gaussian logarithmic Sobolev inequality. Our approach covers several cases involving the strongest possible norm with the optimal exponent, under constraints. Explicit constants are obtained. The strategy of proof relies on entropy methods and the Ornstein-Uhlenbeck flow.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-60" status="VALID">
          <idno type="IdRef">088064239</idno>
          <idno type="ISNI">0000 0004 0645 4046</idno>
          <idno type="RNSR">199712592E</idno>
          <idno type="ROR">https://ror.org/03s0gj002</idno>
          <idno type="Wikidata">Q2913547</idno>
          <orgName>CEntre de REcherches en MAthématiques de la DEcision</orgName>
          <orgName type="acronym">CEREMADE</orgName>
          <date type="start">1971-01-01</date>
          <desc>
            <address>
              <addrLine>Place du Maréchal de Lattre de Tassigny 75775 - Paris Cedex 16</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ceremade.dauphine.fr/index.html</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300302" type="direct"/>
            <relation active="#struct-564132" type="indirect"/>
            <relation name="UMR7534 / URA749" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-1005052" status="VALID">
          <idno type="IdRef">099222221</idno>
          <idno type="ISNI">0000000101748385</idno>
          <idno type="RNSR">199712644L</idno>
          <idno type="ROR">https://ror.org/04xmteb38</idno>
          <orgName>Laboratoire Jacques-Louis Lions</orgName>
          <orgName type="acronym">LJLL (UMR_7598)</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <addrLine>Sorbonne-Université, Boîte courrier 187 - 75252 Paris Cedex 05</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.ljll.math.upmc.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-413221" type="direct"/>
            <relation name="UMR7598" active="#struct-441569" type="direct"/>
            <relation name="UMR_7598" active="#struct-557826" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300302" status="VALID">
          <idno type="IdRef">027787109</idno>
          <idno type="ISNI">0000000120977052</idno>
          <idno type="ROR">https://ror.org/052bz7812</idno>
          <idno type="Wikidata">Q1546437</idno>
          <orgName>Université Paris Dauphine-PSL</orgName>
          <desc>
            <address>
              <addrLine>Place du Maréchal de Lattre de Tassigny75775 PARIS Cedex 16</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://dauphine.psl.eu/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-564132" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-564132" status="VALID">
          <idno type="IdRef">241597595</idno>
          <idno type="ISNI">0000 0004 1784 3645</idno>
          <idno type="ROR">https://ror.org/013cjyk83</idno>
          <orgName>Université Paris Sciences et Lettres</orgName>
          <orgName type="acronym">PSL</orgName>
          <desc>
            <address>
              <addrLine>60 rue Mazarine 75006 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.psl.eu/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-413221" status="VALID">
          <idno type="IdRef">221333754</idno>
          <idno type="ROR">https://ror.org/02en5vm52</idno>
          <orgName>Sorbonne Université</orgName>
          <orgName type="acronym">SU</orgName>
          <date type="start">2018-01-01</date>
          <desc>
            <address>
              <addrLine>21 rue de l’École de médecine - 75006 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.sorbonne-universite.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-557826" status="VALID">
          <idno type="IdRef">236453505</idno>
          <idno type="ISNI">0000 0004 7885 7602</idno>
          <idno type="ROR">https://ror.org/05f82e368</idno>
          <orgName>Université Paris Cité</orgName>
          <orgName type="acronym">UPCité</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <addrLine>85 boulevard Saint-Germain75006 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://u-paris.fr/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>