<?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-02266669v3</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="2026-05-23T20:34:08+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Topological expansion in isomorphism theorems between matrix-valued fields and random walks</title>
            <author role="aut">
              <persName>
                <forename type="first">Titus</forename>
                <surname>Lupu</surname>
              </persName>
              <email type="md5">599898fa0ae109eca6bae26c04d0a61c</email>
              <email type="domain">upmc.fr</email>
              <idno type="idhal" notation="string">titus-lupu</idno>
              <idno type="idhal" notation="numeric">18567</idno>
              <idno type="halauthorid" notation="string">17268-18567</idno>
              <idno type="IDREF">https://www.idref.fr/185397816</idno>
              <idno type="ORCID">https://orcid.org/0000-0001-9770-8010</idno>
              <affiliation ref="#struct-441569"/>
              <affiliation ref="#struct-302352"/>
              <affiliation ref="#struct-1004954"/>
              <affiliation ref="#struct-413221"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Titus</forename>
                <surname>Lupu</surname>
              </persName>
              <email type="md5">599898fa0ae109eca6bae26c04d0a61c</email>
              <email type="domain">upmc.fr</email>
            </editor>
            <funder ref="#projanr-42444"/>
          </titleStmt>
          <editionStmt>
            <edition n="v1">
              <date type="whenSubmitted">2019-08-15 18:41:46</date>
            </edition>
            <edition n="v2">
              <date type="whenSubmitted">2020-02-25 23:47:12</date>
            </edition>
            <edition n="v3" type="current">
              <date type="whenSubmitted">2021-08-02 13:45:07</date>
              <date type="whenWritten">2019-08-13</date>
              <date type="whenModified">2026-03-09 12:48:07</date>
              <date type="whenReleased">2021-08-02 16:52:44</date>
              <date type="whenProduced">2022-05</date>
              <date type="whenEndEmbargoed">2021-08-02</date>
              <ref type="file" target="https://hal.science/hal-02266669v3/document">
                <date notBefore="2021-08-02"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-02266669v3/file/Topo_expansion_isomorphisms_2021.pdf" id="file-3312429-2904269">
                <date notBefore="2021-08-02"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/1908.06732"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="180770">
                <persName>
                  <forename>Titus</forename>
                  <surname>Lupu</surname>
                </persName>
                <email type="md5">599898fa0ae109eca6bae26c04d0a61c</email>
                <email type="domain">upmc.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-02266669</idno>
            <idno type="halUri">https://hal.science/hal-02266669</idno>
            <idno type="halBibtex">lupu:hal-02266669</idno>
            <idno type="halRefHtml">&lt;i&gt;Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques&lt;/i&gt;, 2022, 58 (2), pp.695-721. &lt;a target="_blank" href="https://dx.doi.org/10.1214/21-AIHP1198"&gt;&amp;#x27E8;10.1214/21-AIHP1198&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2022, 58 (2), pp.695-721. &amp;#x27E8;10.1214/21-AIHP1198&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-3312429-2904269"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="LPSM" corresp="SORBONNE-UNIVERSITE">Laboratoire de Probabilités, Statistique et Modélisation</idno>
            <idno type="stamp" n="SORBONNE-UNIVERSITE">Sorbonne Université</idno>
            <idno type="stamp" n="SORBONNE-UNIV" corresp="SORBONNE-UNIVERSITE">Sorbonne Université 01/01/2018</idno>
            <idno type="stamp" n="SU-SCIENCES" corresp="SORBONNE-UNIVERSITE">Faculté des Sciences de Sorbonne Université</idno>
            <idno type="stamp" n="UNIV-PARIS">Université Paris Cité</idno>
            <idno type="stamp" n="UNIVERSITE-PARIS" corresp="UNIV-PARIS">Université Paris Cité</idno>
            <idno type="stamp" n="UP-SCIENCES">Université Paris Cité - Faculté des Sciences</idno>
            <idno type="stamp" n="SU-TI">Sorbonne Université - Texte Intégral</idno>
            <idno type="stamp" n="ANR">ANR</idno>
            <idno type="stamp" n="ALLIANCE-SU"> Alliance Sorbonne Université</idno>
            <idno type="stamp" n="SUPRA_MATHS_INFO">Mathématiques + Informatique</idno>
            <idno type="stamp" n="ANR_QUANTIQUE">ANR QUANTIQUE</idno>
            <idno type="stamp" n="ANR_QUANTIQUE_3" corresp="ANR_QUANTIQUE">ANR_QUANTIQUE_3</idno>
          </seriesStmt>
          <notesStmt>
            <note type="commentary">29 pages, 10 figures. Originally called "Topological expansion in Dynkin type isomorphisms for matrix valued fields".</note>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Topological expansion in isomorphism theorems between matrix-valued fields and random walks</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Titus</forename>
                    <surname>Lupu</surname>
                  </persName>
                  <email type="md5">599898fa0ae109eca6bae26c04d0a61c</email>
                  <email type="domain">upmc.fr</email>
                  <idno type="idhal" notation="string">titus-lupu</idno>
                  <idno type="idhal" notation="numeric">18567</idno>
                  <idno type="halauthorid" notation="string">17268-18567</idno>
                  <idno type="IDREF">https://www.idref.fr/185397816</idno>
                  <idno type="ORCID">https://orcid.org/0000-0001-9770-8010</idno>
                  <affiliation ref="#struct-441569"/>
                  <affiliation ref="#struct-302352"/>
                  <affiliation ref="#struct-1004954"/>
                  <affiliation ref="#struct-413221"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="OLD">38274</idno>
                <idno type="issn">0020-2347</idno>
                <title level="j">Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques</title>
                <imprint>
                  <publisher>Institut Henri Poincaré (IHP)</publisher>
                  <biblScope unit="volume">58</biblScope>
                  <biblScope unit="issue">2</biblScope>
                  <biblScope unit="pp">695-721</biblScope>
                  <date type="datePub">2022-05</date>
                  <date type="dateEpub">2022-05</date>
                </imprint>
              </monogr>
              <idno type="arxiv">1908.06732</idno>
              <idno type="doi">10.1214/21-AIHP1198</idno>
              <ref type="publisher">https://projecteuclid.org/journals/annales-de-linstitut-henri-poincare-probabilites-et-statistiques/volume-58/issue-2/Topological-expansion-in-isomorphism-theorems-between-matrix-valued-fields-and/10.1214/21-AIHP1198.full</ref>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">isomorphism theorems</term>
                <term xml:lang="en">Gaussian free field</term>
                <term xml:lang="en">Gaussian orthogonal ensemble</term>
                <term xml:lang="en">topological expansion</term>
                <term xml:lang="en">random walks</term>
                <term xml:lang="en">random matrices</term>
                <term xml:lang="en">matrix integrals</term>
                <term xml:lang="en">holonomy</term>
                <term xml:lang="en">discrete gauge theory</term>
                <term xml:lang="en">ribbon graphs</term>
                <term xml:lang="en">Gaussian symplectic ensemble</term>
                <term xml:lang="en">Wilson loops</term>
                <term xml:lang="en">Gaussian unitary ensemble</term>
                <term xml:lang="en">matrix models</term>
              </keywords>
              <classCode scheme="classification">MSC2020: 60G15, 81T18, 81T25 (primary),  and 60B20, 60J55 (secondary)</classCode>
              <classCode scheme="halDomain" n="math.math-pr">Mathematics [math]/Probability [math.PR]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>We consider Gaussian fields of real symmetric, complex Hermitian or quaternionic Hermitian matrices over an electrical network, and describe how the isomorphisms between these fields and random walks give rise to topological expansions encoded by ribbon graphs. We further consider matrix-valued Gaussian fields twisted by an orthogonal, unitary or symplectic connection. In this case the isomorphisms involve traces of holonomies of the connection along random walk loops parametrized by boundary cycles of ribbon graphs.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <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="institution" xml:id="struct-302352" status="VALID">
          <idno type="IdRef">232435081</idno>
          <idno type="ISNI">000000040387052X</idno>
          <idno type="ROR">https://ror.org/050jcm728</idno>
          <orgName>Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques</orgName>
          <orgName type="acronym">INSMI-CNRS</orgName>
          <date type="start">2009-10-01</date>
          <desc>
            <address>
              <addrLine>CNRS - Campus Gérard Mégie - 3 rue Michel Ange - 75794 Paris cedex 16</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.insmi.cnrs.fr/fr</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-1004954" status="VALID">
          <idno type="IdRef">235620025</idno>
          <idno type="RNSR">201822759P</idno>
          <idno type="ROR">https://ror.org/02vnd0e65</idno>
          <orgName>Laboratoire de Probabilités, Statistique et Modélisation</orgName>
          <orgName type="acronym">LPSM (UMR_8001)</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <addrLine>Campus Jussieu Tour 16-26, 1er étage 4, Place Jussieu 75005 Paris / Bâtiment Sophie Germain 5ème étage Avenue de France 75013 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.lpsm.paris</ref>
          </desc>
          <listRelation>
            <relation name="UMR_8001" active="#struct-413221" type="direct"/>
            <relation name="UMR8001" active="#struct-441569" type="direct"/>
            <relation name="UMR_8001" active="#struct-557826" type="direct"/>
          </listRelation>
        </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>
      <listOrg type="projects">
        <org type="anrProject" xml:id="projanr-42444" status="VALID">
          <idno type="anr">ANR-16-CE93-0003</idno>
          <orgName>MALIN</orgName>
          <desc>Marches aléatoires en interaction</desc>
          <date type="start">2016</date>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>