InforLorV4, Hal, Checkpoint, bibRecord, 003468

Nilpotent adjacency matrices, random graphs, and quantum random variables

Identifieur interne : 003468 ( Hal/Checkpoint ); précédent : 003467; suivant : 003469

Nilpotent adjacency matrices, random graphs, and quantum random variables

Auteurs : René Schott [France] ; Stacey Staples [États-Unis]

Source :

Journal of Physics A: Mathematical and Theoretical [ 1751-8113 ] ; 2008.

RBID : Hal:hal-00136290

Descripteurs français

mix :
- cycles, fermions, paths, quantum computing, random graphs.

Abstract

For fixed $n>0$, the space of finite graphs on $n$ vertices is canonically associated with an abelian, nilpotent-generated subalgebra of the $2n$-particle fermion algebra. using the generators of the subalgebra, an algebraic probability space of "nilpotent adjacency matrices" associated with finite graphs is defined. Each nilpotent adjacency matrix is a quantum random variable whose $m^th$ moment corresponds to the number of $m$-cycles in the graph $G$. Each matrix admits a canonical "quantum decomposition" into a sum of three algebraic random variables: $a = a^\Delta+ a^\Upsilon+a^Lambda$, where $a^\Delta$ is classical while $a^\Upsilon and $a^\Lambda$ are quantum. Moreover, within the algebraic context, the NP problem of cycle enumeration is reduced to matrix multiplication, requiring no more than $n^4$ multiplications within the algebra.

Url:

https://hal.archives-ouvertes.fr/hal-00136290

Links toward previous steps (curation, corpus...)

to stream Hal, to step Corpus: 006C47
to stream Hal, to step Curation: 006C47

Links to Exploration step

Hal:hal-00136290

Le document en format XML

<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="pt">Nilpotent adjacency matrices, random graphs, and quantum random variables</title>
<author><name sortKey="Schott, Rene" sort="Schott, Rene" uniqKey="Schott R" first="René" last="Schott">René Schott</name>
<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-23" status="OLD"><orgName>Institut Élie Cartan de Nancy</orgName>
<orgName type="acronym">IECN</orgName>
<date type="end">2012-12-31</date>
<desc><address><addrLine>Université Henri Poincaré, Campus Scientifique, boulevard des Aiguillettes, 54000 Vandoeuvre-les-Nancy</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.iecn.u-nancy.fr/</ref>
</desc>
<listRelation><relation active="#struct-300293" type="direct"></relation>
<relation active="#struct-300292" type="direct"></relation>
<relation active="#struct-300291" type="direct"></relation>
<relation active="#struct-300009" type="direct"></relation>
<relation name="UMR7502" active="#struct-441569" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-300293" type="direct"><org type="institution" xml:id="struct-300293" status="OLD"><orgName>Institut National Polytechnique de Lorraine</orgName>
<orgName type="acronym">INPL</orgName>
<date type="end">2011-12-31</date>
<desc><address><country key="FR"></country>
</address>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300292" type="direct"><org type="institution" xml:id="struct-300292" status="OLD"><orgName>Université Nancy 2</orgName>
<date type="end">2011-12-31</date>
<desc><address><addrLine>91 avenue de la Libération, BP 454, 54001 Nancy cedex</addrLine>
<country key="FR"></country>
</address>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300291" type="direct"><org type="institution" xml:id="struct-300291" status="OLD"><orgName>Université Henri Poincaré - Nancy 1</orgName>
<orgName type="acronym">UHP</orgName>
<date type="end">2011-12-31</date>
<desc><address><addrLine>24-30 rue Lionnois, BP 60120, 54 003 NANCY cedex, France</addrLine>
<country key="FR"></country>
</address>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300009" type="direct"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
<orgName type="acronym">Inria</orgName>
<desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/en/</ref>
</desc>
</org>
</tutelle>
<tutelle name="UMR7502" active="#struct-441569" type="direct"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno>
<idno type="IdRef">02636817X</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"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
<placeName><settlement type="city">Nancy</settlement>
<region type="region" nuts="2">Grand Est</region>
<region type="old region" nuts="2">Lorraine (région)</region>
</placeName>
<orgName type="university">Institut national polytechnique de Lorraine</orgName>
<orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName>
<placeName><settlement type="city">Nancy</settlement>
<region type="region" nuts="2">Grand Est</region>
<region type="old region" nuts="2">Lorraine (région)</region>
</placeName>
<orgName type="university">Université Nancy 2</orgName>
<orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName>
</affiliation>
</author>
<author><name sortKey="Staples, Stacey" sort="Staples, Stacey" uniqKey="Staples S" first="Stacey" last="Staples">Stacey Staples</name>
<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-25888" status="VALID"><orgName>Department of Mathematics and Statistics - Southern Illinois University</orgName>
<desc><address><addrLine>College of Arts and Sciences ; Southern Illinois University Edwardsville ; Edwardsville, Illinois 62026</addrLine>
<country key="US"></country>
</address>
<ref type="url">http://www.siue.edu/artsandsciences/math/</ref>
</desc>
<listRelation><relation active="#struct-300932" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-300932" type="direct"><org type="institution" xml:id="struct-300932" status="VALID"><orgName>Southern Illinois University Edwardsville</orgName>
<desc><address><country key="FR"></country>
</address>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>États-Unis</country>
</affiliation>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">HAL</idno>
<idno type="RBID">Hal:hal-00136290</idno>
<idno type="halId">hal-00136290</idno>
<idno type="halUri">https://hal.archives-ouvertes.fr/hal-00136290</idno>
<idno type="url">https://hal.archives-ouvertes.fr/hal-00136290</idno>
<date when="2008">2008</date>
<idno type="wicri:Area/Hal/Corpus">006C47</idno>
<idno type="wicri:Area/Hal/Curation">006C47</idno>
<idno type="wicri:Area/Hal/Checkpoint">003468</idno>
<idno type="wicri:explorRef" wicri:stream="Hal" wicri:step="Checkpoint">003468</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title xml:lang="pt">Nilpotent adjacency matrices, random graphs, and quantum random variables</title>
<author><name sortKey="Schott, Rene" sort="Schott, Rene" uniqKey="Schott R" first="René" last="Schott">René Schott</name>
<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-23" status="OLD"><orgName>Institut Élie Cartan de Nancy</orgName>
<orgName type="acronym">IECN</orgName>
<date type="end">2012-12-31</date>
<desc><address><addrLine>Université Henri Poincaré, Campus Scientifique, boulevard des Aiguillettes, 54000 Vandoeuvre-les-Nancy</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.iecn.u-nancy.fr/</ref>
</desc>
<listRelation><relation active="#struct-300293" type="direct"></relation>
<relation active="#struct-300292" type="direct"></relation>
<relation active="#struct-300291" type="direct"></relation>
<relation active="#struct-300009" type="direct"></relation>
<relation name="UMR7502" active="#struct-441569" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-300293" type="direct"><org type="institution" xml:id="struct-300293" status="OLD"><orgName>Institut National Polytechnique de Lorraine</orgName>
<orgName type="acronym">INPL</orgName>
<date type="end">2011-12-31</date>
<desc><address><country key="FR"></country>
</address>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300292" type="direct"><org type="institution" xml:id="struct-300292" status="OLD"><orgName>Université Nancy 2</orgName>
<date type="end">2011-12-31</date>
<desc><address><addrLine>91 avenue de la Libération, BP 454, 54001 Nancy cedex</addrLine>
<country key="FR"></country>
</address>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300291" type="direct"><org type="institution" xml:id="struct-300291" status="OLD"><orgName>Université Henri Poincaré - Nancy 1</orgName>
<orgName type="acronym">UHP</orgName>
<date type="end">2011-12-31</date>
<desc><address><addrLine>24-30 rue Lionnois, BP 60120, 54 003 NANCY cedex, France</addrLine>
<country key="FR"></country>
</address>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300009" type="direct"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
<orgName type="acronym">Inria</orgName>
<desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/en/</ref>
</desc>
</org>
</tutelle>
<tutelle name="UMR7502" active="#struct-441569" type="direct"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno>
<idno type="IdRef">02636817X</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"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
<placeName><settlement type="city">Nancy</settlement>
<region type="region" nuts="2">Grand Est</region>
<region type="old region" nuts="2">Lorraine (région)</region>
</placeName>
<orgName type="university">Institut national polytechnique de Lorraine</orgName>
<orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName>
<placeName><settlement type="city">Nancy</settlement>
<region type="region" nuts="2">Grand Est</region>
<region type="old region" nuts="2">Lorraine (région)</region>
</placeName>
<orgName type="university">Université Nancy 2</orgName>
<orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName>
</affiliation>
</author>
<author><name sortKey="Staples, Stacey" sort="Staples, Stacey" uniqKey="Staples S" first="Stacey" last="Staples">Stacey Staples</name>
<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-25888" status="VALID"><orgName>Department of Mathematics and Statistics - Southern Illinois University</orgName>
<desc><address><addrLine>College of Arts and Sciences ; Southern Illinois University Edwardsville ; Edwardsville, Illinois 62026</addrLine>
<country key="US"></country>
</address>
<ref type="url">http://www.siue.edu/artsandsciences/math/</ref>
</desc>
<listRelation><relation active="#struct-300932" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-300932" type="direct"><org type="institution" xml:id="struct-300932" status="VALID"><orgName>Southern Illinois University Edwardsville</orgName>
<desc><address><country key="FR"></country>
</address>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>États-Unis</country>
</affiliation>
</author>
</analytic>
<series><title level="j">Journal of Physics A: Mathematical and Theoretical</title>
<idno type="ISSN">1751-8113</idno>
<imprint><date type="datePub">2008</date>
</imprint>
</series>
</biblStruct>
</sourceDesc>
</fileDesc>
<profileDesc><textClass><keywords scheme="mix" xml:lang="fr"><term>cycles</term>
<term>fermions</term>
<term>paths</term>
<term>quantum computing</term>
<term>random graphs</term>
</keywords>
</textClass>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">For fixed $n>0$, the space of finite graphs on $n$ vertices is canonically associated with an abelian, nilpotent-generated subalgebra of the $2n$-particle fermion algebra. using the generators of the subalgebra, an algebraic probability space of "nilpotent adjacency matrices" associated with finite graphs is defined. Each nilpotent adjacency matrix is a quantum random variable whose $m^th$ moment corresponds to the number of $m$-cycles in the graph $G$. Each matrix admits a canonical "quantum decomposition" into a sum of three algebraic random variables: $a = a^\Delta+ a^\Upsilon+a^Lambda$, where $a^\Delta$ is classical while $a^\Upsilon and $a^\Lambda$ are quantum. Moreover, within the algebraic context, the NP problem of cycle enumeration is reduced to matrix multiplication, requiring no more than $n^4$ multiplications within the algebra.</div>
</front>
</TEI>
<hal api="V3"><titleStmt><title xml:lang="pt">Nilpotent adjacency matrices, random graphs, and quantum random variables</title>
<author role="aut"><persName><forename type="first">René</forename>
<surname>Schott</surname>
</persName>
<email></email>
<idno type="halauthor">52507</idno>
<affiliation ref="#struct-23"></affiliation>
<affiliation ref="#struct-160"></affiliation>
</author>
<author role="aut"><persName><forename type="first">Stacey</forename>
<surname>Staples</surname>
</persName>
<email>sstaple@siue.edu</email>
<idno type="halauthor">152056</idno>
<affiliation ref="#struct-25888"></affiliation>
</author>
<editor role="depositor"><persName><forename>René</forename>
<surname>Schott</surname>
</persName>
<email>schott@loria.fr</email>
</editor>
</titleStmt>
<editionStmt><edition n="v1" type="current"><date type="whenSubmitted">2007-03-13 11:52:59</date>
<date type="whenModified">2016-05-19 01:04:30</date>
<date type="whenReleased">2007-03-13 14:54:45</date>
<date type="whenProduced">2008</date>
<date type="whenEndEmbargoed">2007-03-13</date>
<ref type="file" target="https://hal.archives-ouvertes.fr/hal-00136290/document"><date notBefore="2007-03-13"></date>
</ref>
<ref type="file" subtype="author" n="1" target="https://hal.archives-ouvertes.fr/hal-00136290/file/2007-08.pdf"><date notBefore="2007-03-13"></date>
</ref>
</edition>
<respStmt><resp>contributor</resp>
<name key="112746"><persName><forename>René</forename>
<surname>Schott</surname>
</persName>
<email>schott@loria.fr</email>
</name>
</respStmt>
</editionStmt>
<publicationStmt><distributor>CCSD</distributor>
<idno type="halId">hal-00136290</idno>
<idno type="halUri">https://hal.archives-ouvertes.fr/hal-00136290</idno>
<idno type="halBibtex">schott:hal-00136290</idno>
<idno type="halRefHtml">Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2008, 41, pp.155-205</idno>
<idno type="halRef">Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2008, 41, pp.155-205</idno>
</publicationStmt>
<seriesStmt><idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
<idno type="stamp" n="IECN">IECN - Institut Elie Cartan Nancy</idno>
<idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
<idno type="stamp" n="INPL">Institut National Polytechnique de Lorraine</idno>
<idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
<idno type="stamp" n="LORIA2">Publications du LORIA</idno>
<idno type="stamp" n="LABO-LORIA-SET" p="LORIA">LABO-LORIA-SET</idno>
<idno type="stamp" n="LORIA">LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications</idno>
<idno type="stamp" n="UNIV-LORRAINE">Université de Lorraine</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="pt">Nilpotent adjacency matrices, random graphs, and quantum random variables</title>
<author role="aut"><persName><forename type="first">René</forename>
<surname>Schott</surname>
</persName>
<idno type="halAuthorId">52507</idno>
<affiliation ref="#struct-23"></affiliation>
<affiliation ref="#struct-160"></affiliation>
</author>
<author role="aut"><persName><forename type="first">Stacey</forename>
<surname>Staples</surname>
</persName>
<email>sstaple@siue.edu</email>
<idno type="halAuthorId">152056</idno>
<affiliation ref="#struct-25888"></affiliation>
</author>
</analytic>
<monogr><idno type="localRef">Prépublication IECN 2007/08</idno>
<idno type="halJournalId" status="VALID">16018</idno>
<idno type="issn">1751-8113</idno>
<idno type="eissn">1751-8121</idno>
<title level="j">Journal of Physics A: Mathematical and Theoretical</title>
<imprint><publisher>IOP Publishing</publisher>
<biblScope unit="volume">41</biblScope>
<biblScope unit="pp">155-205</biblScope>
<date type="datePub">2008</date>
</imprint>
</monogr>
</biblStruct>
</sourceDesc>
<profileDesc><langUsage><language ident="en">English</language>
</langUsage>
<textClass><keywords scheme="author"><term xml:lang="fr">fermions</term>
<term xml:lang="fr">random graphs</term>
<term xml:lang="fr">cycles</term>
<term xml:lang="fr">paths</term>
<term xml:lang="fr">quantum computing</term>
</keywords>
<classCode scheme="classification">60B99 ; 81P68 ; 05C38 ; 05C50 ; 05C80 ; 15A66</classCode>
<classCode scheme="halDomain" n="math.math-pr">Mathematics [math]/Probability [math.PR]</classCode>
<classCode scheme="halTypology" n="ART">Journal articles</classCode>
</textClass>
<abstract xml:lang="en">For fixed $n>0$, the space of finite graphs on $n$ vertices is canonically associated with an abelian, nilpotent-generated subalgebra of the $2n$-particle fermion algebra. using the generators of the subalgebra, an algebraic probability space of "nilpotent adjacency matrices" associated with finite graphs is defined. Each nilpotent adjacency matrix is a quantum random variable whose $m^th$ moment corresponds to the number of $m$-cycles in the graph $G$. Each matrix admits a canonical "quantum decomposition" into a sum of three algebraic random variables: $a = a^\Delta+ a^\Upsilon+a^Lambda$, where $a^\Delta$ is classical while $a^\Upsilon and $a^\Lambda$ are quantum. Moreover, within the algebraic context, the NP problem of cycle enumeration is reduced to matrix multiplication, requiring no more than $n^4$ multiplications within the algebra.</abstract>
</profileDesc>
</hal>
</record>

Pour manipuler ce document sous Unix (Dilib)

EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/Hal/Checkpoint

HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 003468 | SxmlIndent | more

HfdSelect -h $EXPLOR_AREA/Data/Hal/Checkpoint/biblio.hfd -nk 003468 | SxmlIndent | more

Pour mettre un lien sur cette page dans le réseau Wicri

{{Explor lien
   |wiki=    Wicri/Lorraine
   |area=    InforLorV4
   |flux=    Hal
   |étape=   Checkpoint
   |type=    RBID
   |clé=     Hal:hal-00136290
   |texte=   Nilpotent adjacency matrices, random graphs, and quantum random variables
}}

This area was generated with Dilib version V0.6.33.
Data generation: Mon Jun 10 21:56:28 2019. Site generation: Fri Feb 25 15:29:27 2022

	Serveur d'exploration sur la recherche en informatique en Lorraine
	Attention, ce site est en cours de développement ! Attention, site généré par des moyens informatiques à partir de corpus bruts. Les informations ne sont donc pas validées.

Serveur d'exploration sur la recherche en informatique en Lorraine

Nilpotent adjacency matrices, random graphs, and quantum random variables

Nilpotent adjacency matrices, random graphs, and quantum random variables

Source :

Descripteurs français

Abstract

Links toward previous steps (curation, corpus...)

Links to Exploration step

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri