<?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-00134275</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="2026-05-20T06:19:15+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Noise corrections to stochastic trace formulas</title>
            <author role="aut">
              <persName>
                <forename type="first">G.</forename>
                <surname>Palla</surname>
              </persName>
              <email type="md5">ee27eb0f34aca9dbf9c0f11c9edd8329</email>
              <email type="domain">galahad.elte.hu</email>
              <idno type="idhal" notation="numeric">838522</idno>
              <idno type="halauthorid" notation="string">83771-838522</idno>
              <orgName ref="#struct-210634"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">G.</forename>
                <surname>Vattay</surname>
              </persName>
              <email type="md5">9982d716dfd32b6efee40d2832c2872d</email>
              <email type="domain">robin.elte.hu</email>
              <idno type="idhal" notation="numeric">838523</idno>
              <idno type="halauthorid" notation="string">64196-838523</idno>
              <orgName ref="#struct-210634"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">André</forename>
                <surname>Voros</surname>
              </persName>
              <email type="md5">209163f9befa657fd89b1440adbdfef1</email>
              <email type="domain">cea.fr</email>
              <idno type="idhal" notation="numeric">832921</idno>
              <idno type="halauthorid" notation="string">136172-832921</idno>
              <affiliation ref="#struct-113"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">N.</forename>
                <surname>Søndergaard</surname>
              </persName>
              <idno type="halauthorid">195897-0</idno>
              <orgName ref="#struct-0"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">C.P.</forename>
                <surname>Dettmann</surname>
              </persName>
              <idno type="halauthorid">195898-0</idno>
              <orgName ref="#struct-0"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Marcel P.</forename>
                <surname>Gingold</surname>
              </persName>
              <email type="md5">0d07f540105995e5afe3eed3c2ca4771</email>
              <email type="domain">gmail.com</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2007-03-01 14:16:49</date>
              <date type="whenWritten">2001-01</date>
              <date type="whenModified">2024-04-03 10:20:11</date>
              <date type="whenReleased">2007-03-01 14:17:43</date>
              <date type="whenProduced">2001</date>
              <ref type="externalLink" target="http://arxiv.org/pdf/nlin.CD/0101045"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="104194">
                <persName>
                  <forename>Marcel P.</forename>
                  <surname>Gingold</surname>
                </persName>
                <email type="md5">0d07f540105995e5afe3eed3c2ca4771</email>
                <email type="domain">gmail.com</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00134275</idno>
            <idno type="halUri">https://hal.science/hal-00134275</idno>
            <idno type="halBibtex">palla:hal-00134275</idno>
            <idno type="halRefHtml">&lt;i&gt;Foundations of Physics&lt;/i&gt;, 2001, 31, pp.641-657</idno>
            <idno type="halRef">Foundations of Physics, 2001, 31, pp.641-657</idno>
            <availability status="restricted"/>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="CEA">CEA - Commissariat à l'énergie atomique</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="DSM-IPHT" corresp="CEA">IPHT</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="CEA-DRF" corresp="CEA">Direction de Recherche Fondamentale</idno>
          </seriesStmt>
          <notesStmt>
            <note type="commentary">URL: http://www-spht.cea.fr/articles/T00/181 (sur invitation). Corrections de bruit aux formules de trace stochastiques</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">Noise corrections to stochastic trace formulas</title>
                <author role="aut">
                  <persName>
                    <forename type="first">G.</forename>
                    <surname>Palla</surname>
                  </persName>
                  <email type="md5">ee27eb0f34aca9dbf9c0f11c9edd8329</email>
                  <email type="domain">galahad.elte.hu</email>
                  <idno type="idhal" notation="numeric">838522</idno>
                  <idno type="halauthorid" notation="string">83771-838522</idno>
                  <orgName ref="#struct-210634"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">G.</forename>
                    <surname>Vattay</surname>
                  </persName>
                  <email type="md5">9982d716dfd32b6efee40d2832c2872d</email>
                  <email type="domain">robin.elte.hu</email>
                  <idno type="idhal" notation="numeric">838523</idno>
                  <idno type="halauthorid" notation="string">64196-838523</idno>
                  <orgName ref="#struct-210634"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">André</forename>
                    <surname>Voros</surname>
                  </persName>
                  <email type="md5">209163f9befa657fd89b1440adbdfef1</email>
                  <email type="domain">cea.fr</email>
                  <idno type="idhal" notation="numeric">832921</idno>
                  <idno type="halauthorid" notation="string">136172-832921</idno>
                  <affiliation ref="#struct-113"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">N.</forename>
                    <surname>Søndergaard</surname>
                  </persName>
                  <idno type="halauthorid">195897-0</idno>
                  <orgName ref="#struct-0"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">C.P.</forename>
                    <surname>Dettmann</surname>
                  </persName>
                  <idno type="halauthorid">195898-0</idno>
                  <orgName ref="#struct-0"/>
                </author>
              </analytic>
              <monogr>
                <idno type="localRef">SPhT-T00/181</idno>
                <idno type="halJournalId" status="VALID">4940</idno>
                <idno type="issn">0015-9018</idno>
                <idno type="eissn">1572-9516</idno>
                <title level="j">Foundations of Physics</title>
                <imprint>
                  <publisher>Springer Verlag</publisher>
                  <biblScope unit="volume">31</biblScope>
                  <biblScope unit="pp">641-657</biblScope>
                  <date type="datePub">2001</date>
                </imprint>
              </monogr>
              <idno type="arxiv">nlin.CD/0101045</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="halDomain" n="phys.phys.phys-gen-ph">Physics [physics]/Physics [physics]/General Physics [physics.gen-ph]</classCode>
              <classCode scheme="halDomain" n="nlin.nlin-cd">Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD]</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 review studies of an evolution operator ${\cal L}$ for a discrete Langevin equation with a strongly hyperbolic classical dynamics and a Gaussian noise. The leading eigenvalue of ${\cal L}$ yields a physically measurable property of the dynamical system, the escape rate from the repeller. The spectrum of the evolution operator ${\cal L}$ in the weak noise limit can be computed in several ways. A method using a local matrix representation of the operator allows to push the corrections to the escape rate up to order eight in the noise expansion parameter. These corrections then appear to form a divergent series. Actually, via a cumulant expansion, they relate to analogous divergent series for other quantities, the traces of the evolution operators ${\cal L}^n$. Using an integral representation of the evolution operator ${\cal L},$ we then investigate the high order corrections to the latter traces. Their asymptotic behavior is found to be controlled by sub-dominant saddle points previously neglected in the perturbative expansion, and to be ultimately described by a kind of trace formula.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-113" status="OLD">
          <orgName>Service de Physique Théorique</orgName>
          <orgName type="acronym">SPhT</orgName>
          <desc>
            <address>
              <addrLine>CEA/Saclay - 91191 Gif-sur-Yvette Cedex, France</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www-spht.cea.fr/fr/</ref>
          </desc>
          <listRelation>
            <relation name="DSM/SPHT" active="#struct-300016" type="direct"/>
            <relation name="URA2306" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300016" status="VALID">
          <idno type="IdRef">026372061</idno>
          <idno type="ISNI">0000000122998025</idno>
          <idno type="ROR">https://ror.org/00jjx8s55</idno>
          <idno type="Wikidata">Q868550</idno>
          <orgName>Commissariat à l'énergie atomique et aux énergies alternatives</orgName>
          <orgName type="acronym">CEA</orgName>
          <desc>
            <address>
              <addrLine>Centre de SaclayCentre de GrenobleCentre de Cadaracheetc</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.cea.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>