<?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-05337525</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="2026-05-02T01:40:50+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Large time cumulants of the KPZ equation on an interval</title>
            <author role="aut">
              <persName>
                <forename type="first">Guillaume</forename>
                <surname>Barraquand</surname>
              </persName>
              <email type="md5">fc03ca4ea7716d8afb19883754f933fe</email>
              <email type="domain">gmail.com</email>
              <idno type="idhal" notation="string">guillaume-barraquand</idno>
              <idno type="idhal" notation="numeric">176756</idno>
              <idno type="halauthorid" notation="string">26050-176756</idno>
              <idno type="ARXIV">https://arxiv.org/a/barraquand_g_1</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-0082-7510</idno>
              <idno type="GOOGLE SCHOLAR">https://scholar.google.com/citations?user=TFgA5nMAAAAJ&amp;hl=fr</idno>
              <affiliation ref="#struct-1085043"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Pierre</forename>
                <surname>Le Doussal</surname>
              </persName>
              <email type="md5">bc5c68c0ba592b83801b95b1c0c30eb4</email>
              <email type="domain">lpt.ens.fr</email>
              <idno type="idhal" notation="numeric">841500</idno>
              <idno type="halauthorid" notation="string">103094-841500</idno>
              <idno type="ORCID">https://orcid.org/0000-0001-6052-1922</idno>
              <affiliation ref="#struct-1085043"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Guillaume</forename>
                <surname>Barraquand</surname>
              </persName>
              <email type="md5">b9406733ea0b621e34bee7b53831b972</email>
              <email type="domain">math.cnrs.fr</email>
            </editor>
            <funder ref="#projanr-57087"/>
            <funder ref="#projanr-102841"/>
            <funder ref="#projanr-103002"/>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2025-10-29 16:39:52</date>
              <date type="whenModified">2026-03-13 10:10:02</date>
              <date type="whenReleased">2025-10-30 10:15:46</date>
              <date type="whenProduced">2025-08-06</date>
              <date type="whenEndEmbargoed">2025-10-29</date>
              <ref type="file" target="https://hal.science/hal-05337525v1/document">
                <date notBefore="2025-10-29"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-05337525v1/file/2504.18292v3.pdf" id="file-5337525-4570143">
                <date notBefore="2025-10-29"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/2504.18292"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="317882">
                <persName>
                  <forename>Guillaume</forename>
                  <surname>Barraquand</surname>
                </persName>
                <email type="md5">b9406733ea0b621e34bee7b53831b972</email>
                <email type="domain">math.cnrs.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-05337525</idno>
            <idno type="halUri">https://hal.science/hal-05337525</idno>
            <idno type="halBibtex">barraquand:hal-05337525</idno>
            <idno type="halRefHtml">&lt;i&gt;Journal of Statistical Physics&lt;/i&gt;, 2025, 192 (8), pp.111. &lt;a target="_blank" href="https://dx.doi.org/10.1007/s10955-025-03496-9"&gt;&amp;#x27E8;10.1007/s10955-025-03496-9&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Journal of Statistical Physics, 2025, 192 (8), pp.111. &amp;#x27E8;10.1007/s10955-025-03496-9&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-5337525-4570143"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="ENS-PARIS">Ecole Normale Supérieure de Paris</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="TDS-MACS">Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes</idno>
            <idno type="stamp" n="PSL">Université Paris sciences et lettres</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="LPENS" corresp="ENS-PARIS">Laboratoire de physique de l'ENS</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="ENS-PSL" corresp="PSL">École normale supérieure - PSL</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="ANR_QUANTIQUE">ANR QUANTIQUE</idno>
            <idno type="stamp" n="ANR_QUANTIQUE_4" corresp="ANR_QUANTIQUE">ANR_QUANTIQUE_4</idno>
          </seriesStmt>
          <notesStmt>
            <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">Large time cumulants of the KPZ equation on an interval</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Guillaume</forename>
                    <surname>Barraquand</surname>
                  </persName>
                  <email type="md5">fc03ca4ea7716d8afb19883754f933fe</email>
                  <email type="domain">gmail.com</email>
                  <idno type="idhal" notation="string">guillaume-barraquand</idno>
                  <idno type="idhal" notation="numeric">176756</idno>
                  <idno type="halauthorid" notation="string">26050-176756</idno>
                  <idno type="ARXIV">https://arxiv.org/a/barraquand_g_1</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-0082-7510</idno>
                  <idno type="GOOGLE SCHOLAR">https://scholar.google.com/citations?user=TFgA5nMAAAAJ&amp;hl=fr</idno>
                  <affiliation ref="#struct-1085043"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Pierre</forename>
                    <surname>Le Doussal</surname>
                  </persName>
                  <email type="md5">bc5c68c0ba592b83801b95b1c0c30eb4</email>
                  <email type="domain">lpt.ens.fr</email>
                  <idno type="idhal" notation="numeric">841500</idno>
                  <idno type="halauthorid" notation="string">103094-841500</idno>
                  <idno type="ORCID">https://orcid.org/0000-0001-6052-1922</idno>
                  <affiliation ref="#struct-1085043"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">16250</idno>
                <idno type="issn">0022-4715</idno>
                <idno type="eissn">1572-9613</idno>
                <title level="j">Journal of Statistical Physics</title>
                <imprint>
                  <publisher>Springer Verlag</publisher>
                  <biblScope unit="volume">192</biblScope>
                  <biblScope unit="issue">8</biblScope>
                  <biblScope unit="pp">111</biblScope>
                  <date type="datePub">2025-08-06</date>
                </imprint>
              </monogr>
              <idno type="arxiv">2504.18292</idno>
              <idno type="doi">10.1007/s10955-025-03496-9</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="halDomain" n="phys.mphy">Physics [physics]/Mathematical Physics [math-ph]</classCode>
              <classCode scheme="halDomain" n="math.math-pr">Mathematics [math]/Probability [math.PR]</classCode>
              <classCode scheme="halDomain" n="phys.cond.cm-sm">Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech]</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 the Kardar-Parisi-Zhang equation on the interval $[0,L]$ with Neumann type boundary conditions and boundary parameters $u,v$.  We show that the $k$-th order cumulant of the height behaves as $c_k(L,u,v)\,  t$ in the large time limit $t \to +\infty$, and we compute the coefficients $c_k(L,u,v)$. We obtain an expression for  the upper tail large deviation function of the height. We also consider the limit of large $L$, with $u=\tilde u/\sqrt{L}$, $u=\tilde v/\sqrt{L}$, which should give the same quantities for the two parameter family $(\tilde u, \tilde v)$ KPZ fixed point on the interval.  We employ two complementary methods. On the one hand we adapt to the interval the replica Bethe ansatz method pioneered by Brunet and Derrida for the periodic case. On the other hand, we perform a scaling limit using previous results available for the open ASEP. The latter method allows to  express the cumulants of the KPZ equation in terms a functional equation involving an integral operator.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="researchteam" xml:id="struct-1085043" status="VALID">
          <orgName>Physique des Fluctuations, des Corrélations et de l'Information</orgName>
          <date type="start">2022-01-01</date>
          <desc>
            <address>
              <addrLine>LPENS (UMR 8023) -Département de Physique de l'ENS-PSL -24 rue Lhomond -75005 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.lpens.ens.psl.eu/recherche/phystat/equipe-04/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-1004921" type="direct"/>
            <relation active="#struct-413221" type="indirect"/>
            <relation name="UMR8023" active="#struct-441569" type="indirect"/>
            <relation active="#struct-557826" type="indirect"/>
            <relation active="#struct-1136774" type="indirect"/>
            <relation active="#struct-59704" type="indirect"/>
            <relation active="#struct-564132" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-1004921" status="VALID">
          <idno type="IdRef">192153935</idno>
          <idno type="RNSR">201922973T</idno>
          <idno type="ROR">https://ror.org/03a26mh11</idno>
          <orgName>Laboratoire de physique de l'ENS - ENS Paris</orgName>
          <orgName type="acronym">LPENS</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <addrLine>24, rue Lhomond75005 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.lpens.ens.psl.eu/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-413221" type="direct"/>
            <relation name="UMR8023" active="#struct-441569" type="direct"/>
            <relation active="#struct-557826" type="direct"/>
            <relation active="#struct-1136774" type="direct"/>
            <relation active="#struct-59704" type="indirect"/>
            <relation active="#struct-564132" type="indirect"/>
          </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="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-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>
        <org type="regrouplaboratory" xml:id="struct-1136774" status="VALID">
          <orgName>Département de Physique de l'ENS-PSL</orgName>
          <desc>
            <address>
              <addrLine>24 rue Lhomond, 75005 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.phys.ens.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-59704" type="direct"/>
            <relation active="#struct-564132" type="indirect"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-59704" status="VALID">
          <idno type="IdRef">031738419</idno>
          <idno type="ISNI">0000000123532622</idno>
          <idno type="ROR">https://ror.org/05a0dhs15</idno>
          <orgName>École normale supérieure - Paris</orgName>
          <orgName type="acronym">ENS-PSL</orgName>
          <date type="start">1985-07-24</date>
          <desc>
            <address>
              <addrLine>45, Rue d'Ulm - 75230 Paris cedex 05</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.ens.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>
      </listOrg>
      <listOrg type="projects">
        <org type="anrProject" xml:id="projanr-57087" status="VALID">
          <idno type="anr">ANR-21-CE40-0019</idno>
          <orgName>CORTIPOM</orgName>
          <desc>Théorie combinatoire des représentations et interactions avec des modèles probabilistes</desc>
          <date type="start">2021</date>
        </org>
        <org type="anrProject" xml:id="projanr-102841" status="VALID">
          <idno type="anr">ANR-23-ERCB-0007</idno>
          <orgName>IntStoch</orgName>
          <desc>Modèles intégrables stochastiques : chemins non-intersectants, interfaces et diffusions en milieu aléatoire</desc>
          <date type="start">2023</date>
        </org>
        <org type="anrProject" xml:id="projanr-103002" status="VALID">
          <idno type="anr">ANR-23-CE30-0020</idno>
          <orgName>EDIPS</orgName>
          <desc>Dynamique des extrêmes dans les systèmes de particules en interaction</desc>
          <date type="start">2023</date>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>