<?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-01286177</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="2026-05-20T09:52:23+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">$W_{1,+}$-interpolation of probability measures on graphs</title>
            <author role="aut">
              <persName>
                <forename type="first">Erwan</forename>
                <surname>Hillion</surname>
              </persName>
              <email type="md5">c30c88da704a458037ebbdedd1dffc71</email>
              <email type="domain">univ-amu.fr</email>
              <idno type="idhal" notation="numeric">978216</idno>
              <idno type="halauthorid" notation="string">1007202-978216</idno>
              <affiliation ref="#struct-241321"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Erwan</forename>
                <surname>Hillion</surname>
              </persName>
              <email type="md5">c30c88da704a458037ebbdedd1dffc71</email>
              <email type="domain">univ-amu.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2016-03-10 14:10:04</date>
              <date type="whenModified">2024-04-26 13:18:28</date>
              <date type="whenReleased">2016-03-11 11:21:58</date>
              <date type="whenProduced">2016-03-10</date>
              <date type="whenEndEmbargoed">2016-03-10</date>
              <ref type="file" target="https://hal.science/hal-01286177v1/document">
                <date notBefore="2016-03-10"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-01286177v1/file/1402.3438v1.pdf" id="file-1286177-1366014">
                <date notBefore="2016-03-10"/>
              </ref>
              <ref type="externalLink" target="https://doi.org/10.1214/ejp.v19-3336"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="335423">
                <persName>
                  <forename>Erwan</forename>
                  <surname>Hillion</surname>
                </persName>
                <email type="md5">c30c88da704a458037ebbdedd1dffc71</email>
                <email type="domain">univ-amu.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-01286177</idno>
            <idno type="halUri">https://hal.science/hal-01286177</idno>
            <idno type="halBibtex">hillion:hal-01286177</idno>
            <idno type="halRefHtml">2016</idno>
            <idno type="halRef">2016</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-1286177-1366014"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="UNIV-AMU">Aix Marseille Université</idno>
            <idno type="stamp" n="EC-MARSEILLE">Ecole Centrale de Marseille</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="I2M">Institut de Mathématiques de Marseille</idno>
            <idno type="stamp" n="I2M-2014-" corresp="I2M">Institut de Mathématiques de Marseille 2014-</idno>
          </seriesStmt>
          <notesStmt/>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">$W_{1,+}$-interpolation of probability measures on graphs</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Erwan</forename>
                    <surname>Hillion</surname>
                  </persName>
                  <email type="md5">c30c88da704a458037ebbdedd1dffc71</email>
                  <email type="domain">univ-amu.fr</email>
                  <idno type="idhal" notation="numeric">978216</idno>
                  <idno type="halauthorid" notation="string">1007202-978216</idno>
                  <affiliation ref="#struct-241321"/>
                </author>
              </analytic>
              <monogr>
                <imprint/>
              </monogr>
              <idno type="doi">10.1214/EJP.v19-3336</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="halDomain" n="math.math-pr">Mathematics [math]/Probability [math.PR]</classCode>
              <classCode scheme="halTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halOldTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halTreeTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>We generalize an equation introduced by Benamou and Brenier in [BB00] and characterizing Wasserstein Wp-geodesics for p &gt; 1, from the continuous setting of probability distributions on a Riemannian manifold to the discrete setting of probability distributions on a general graph. Given an initial and a final distributions (f0(x))x∈G, (f1(x))x∈G, we prove the existence of a curve (ft(k)) t∈[0,1],k∈Z satisfying this Benamou-Brenier equation. We also show that such a curve can be described as a mixture of binomial distributions with respect to a coupling that is solution of a certain optimization problem.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-241321" status="VALID">
          <idno type="RNSR">201420768T</idno>
          <idno type="ROR">042h2y225</idno>
          <orgName>Institut de Mathématiques de Marseille</orgName>
          <orgName type="acronym">I2M</orgName>
          <date type="start">2014</date>
          <desc>
            <address>
              <addrLine>Centre de Mathématiques et Informatique (CMI)Technopôle Château-Gombert39, rue Frédéric Joliot Curie13453 Marseille Cedex 13</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.i2m.univ-amu.fr/</ref>
          </desc>
          <listRelation>
            <relation name="UMR7373" active="#struct-198056" type="direct"/>
            <relation name="UMR7373" active="#struct-300415" type="direct"/>
            <relation name="UMR7373" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-198056" status="VALID">
          <idno type="IdRef">15863621X</idno>
          <idno type="ISNI">0000 0001 2176 4817</idno>
          <idno type="ROR">https://ror.org/035xkbk20</idno>
          <orgName>Aix Marseille Université</orgName>
          <orgName type="acronym">AMU</orgName>
          <date type="start">2012-01-01</date>
          <desc>
            <address>
              <addrLine>Aix-Marseille UniversitéJardins du Pharo58 Boulevard Charles Livon13284 Marseille cedex 7</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-amu.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300415" status="VALID">
          <idno type="ISNI">0000 0004 1762 2703</idno>
          <idno type="ROR">https://ror.org/040baw385</idno>
          <orgName>École Centrale de Marseille</orgName>
          <orgName type="acronym">ECM</orgName>
          <date type="start">2006-09-27</date>
          <desc>
            <address>
              <addrLine>Pôle de l'étoile - Technopole de Château-Gombert - 38 rue Frédéric Joliot-Curie - 13013 Marseille</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.centrale-marseille.fr/</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>
      </listOrg>
    </back>
  </text>
</TEI>