InforLorV4, PascalFrancis, Corpus, bibRecord, 000315

Nilpotent adjacency matrices, random graphs and quantum random variables

Identifieur interne : 000315 ( PascalFrancis/Corpus ); précédent : 000314; suivant : 000316

Nilpotent adjacency matrices, random graphs and quantum random variables

Auteurs : René Schott ; George Stacey Staples

Source :

Journal of physics. A, Mathematical and theoretical : (Print) [ 1751-8113 ] ; 2008.

RBID : Pascal:08-0216287

Descripteurs français

Pascal (Inist)
- Matrice aléatoire, Graphe aléatoire, Graphe quantique, Variable aléatoire, Théorie quantique, Probabilité, Graphe fini, Fermion, Opérateur annihilation, Dimension infinie, Vertex, Chaîne Markov.

English descriptors

KwdEn :
- Annihilation operators, Fermions, Finite graph, Infinite dimension, Markov chain, Probability, Quantum graph, Quantum theory, Random graph, Random matrix, Random variable, Vertex.

Abstract

While a number of researchers have previously investigated the relationship between graph theory and quantum probability, the current work explores a new perspective. The approach of this paper is to begin with an arbitrary graph having no previously established relationship to quantum probability and to use that graph to construct a quantum probability space in which moments of quantum random variables reveal information about the graph's structure. Given an arbitrary finite graph and arbitrary odd integer m≥ 3, fermion annihilation operators are used to construct a family of quantum random variables whose mth moments correspond to the graph's m-cycles. The approach is then generalized to recover a graph's m-cycles for any integer m≥ 3 by defining nilpotent adjacency operators in terms of null-square generators of an infinite-dimensional Abelian algebra. It is shown that ordering the vertices of a simple graph induces a canonical decompositionΨ =Ψ⁺ + Ψ^- on any nilpotent adjacency operator Ψ. The work concludes with applications to Markov chains and random graphs.

Notice en format standard (ISO 2709)

Pour connaître la documentation sur le format Inist Standard.

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A03		`1`		`@0 J. phys., A, math. theor. : (Print)`
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A08	`01`	`1`	`ENG`	`@1 Nilpotent adjacency matrices, random graphs and quantum random variables`
A11	`01`	`1`		`@1 SCHOTT (René)`
A11	`02`	`1`		`@1 STACEY STAPLES (George)`
A14	`01`			`@1 IECN and LORIA Université Henri Poincaré-Nancy I, BP 239 @2 54506 Vandoeuvre-lès-Nancy @3 FRA @Z 1 aut.`
A14	`02`			`@1 Department of Mathematics and Statistics, Southern Illinois University Edwardsville @2 Edwardsville, IL 62026-1653 @3 USA @Z 2 aut.`
A20				`@2 155205.1-155205.16`
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A44				`@0 0000 @1 © 2008 INIST-CNRS. All rights reserved.`
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A64	`01`	`1`		`@0 Journal of physics. A, Mathematical and theoretical : (Print)`
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C01	`01`		`ENG`	@0 While a number of researchers have previously investigated the relationship between graph theory and quantum probability, the current work explores a new perspective. The approach of this paper is to begin with an arbitrary graph having no previously established relationship to quantum probability and to use that graph to construct a quantum probability space in which moments of quantum random variables reveal information about the graph's structure. Given an arbitrary finite graph and arbitrary odd integer m≥ 3, fermion annihilation operators are used to construct a family of quantum random variables whose mth moments correspond to the graph's m-cycles. The approach is then generalized to recover a graph's m-cycles for any integer m≥ 3 by defining nilpotent adjacency operators in terms of null-square generators of an infinite-dimensional Abelian algebra. It is shown that ordering the vertices of a simple graph induces a canonical decompositionΨ =Ψ⁺ + Ψ^- on any nilpotent adjacency operator Ψ. The work concludes with applications to Markov chains and random graphs.
C02	`01`	`3`		`@0 001B00`
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C03	`07`	`X`	`FRE`	`@0 Graphe fini @5 32`
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C03	`08`	`3`	`FRE`	`@0 Fermion @5 33`
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C03	`09`	`3`	`FRE`	`@0 Opérateur annihilation @5 34`
C03	`09`	`3`	`ENG`	`@0 Annihilation operators @5 34`
C03	`10`	`X`	`FRE`	`@0 Dimension infinie @5 35`
C03	`10`	`X`	`ENG`	`@0 Infinite dimension @5 35`
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C03	`11`	`X`	`FRE`	`@0 Vertex @5 36`
C03	`11`	`X`	`ENG`	`@0 Vertex @5 36`
C03	`11`	`X`	`SPA`	`@0 Vértice @5 36`
C03	`12`	`X`	`FRE`	`@0 Chaîne Markov @5 37`
C03	`12`	`X`	`ENG`	`@0 Markov chain @5 37`
C03	`12`	`X`	`SPA`	`@0 Cadena Markov @5 37`
N21				`@1 140`
N44	`01`			`@1 OTO`
N82				`@1 OTO`

Format Inist (serveur)

NO :	PASCAL 08-0216287 INIST
ET :	Nilpotent adjacency matrices, random graphs and quantum random variables
AU :	SCHOTT (René); STACEY STAPLES (George)
AF :	IECN and LORIA Université Henri Poincaré-Nancy I, BP 239/54506 Vandoeuvre-lès-Nancy/France (1 aut.); Department of Mathematics and Statistics, Southern Illinois University Edwardsville/Edwardsville, IL 62026-1653/Etats-Unis (2 aut.)
DT :	Publication en série; Niveau analytique
SO :	Journal of physics. A, Mathematical and theoretical : (Print); ISSN 1751-8113; Royaume-Uni; Da. 2008; Vol. 41; No. 15; 155205.1-155205.16; Bibl. 20 ref.
LA :	Anglais
EA :	While a number of researchers have previously investigated the relationship between graph theory and quantum probability, the current work explores a new perspective. The approach of this paper is to begin with an arbitrary graph having no previously established relationship to quantum probability and to use that graph to construct a quantum probability space in which moments of quantum random variables reveal information about the graph's structure. Given an arbitrary finite graph and arbitrary odd integer m≥ 3, fermion annihilation operators are used to construct a family of quantum random variables whose mth moments correspond to the graph's m-cycles. The approach is then generalized to recover a graph's m-cycles for any integer m≥ 3 by defining nilpotent adjacency operators in terms of null-square generators of an infinite-dimensional Abelian algebra. It is shown that ordering the vertices of a simple graph induces a canonical decompositionΨ =Ψ⁺ + Ψ^- on any nilpotent adjacency operator Ψ. The work concludes with applications to Markov chains and random graphs.
CC :	001B00
FD :	Matrice aléatoire; Graphe aléatoire; Graphe quantique; Variable aléatoire; Théorie quantique; Probabilité; Graphe fini; Fermion; Opérateur annihilation; Dimension infinie; Vertex; Chaîne Markov
ED :	Random matrix; Random graph; Quantum graph; Random variable; Quantum theory; Probability; Finite graph; Fermions; Annihilation operators; Infinite dimension; Vertex; Markov chain
SD :	Matriz aleatoria; Grafo aleatorio; Grafo cuántico; Variable aléatoria; Grafo finito; Dimensión infinita; Vértice; Cadena Markov
LO :	INIST-577C.354000172636590090
ID :	08-0216287

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Pascal:08-0216287

Le document en format XML

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<ET>Nilpotent adjacency matrices, random graphs and quantum random variables</ET>
<AU>SCHOTT (René); STACEY STAPLES (George)</AU>
<AF>IECN and LORIA Université Henri Poincaré-Nancy I, BP 239/54506 Vandoeuvre-lès-Nancy/France (1 aut.); Department of Mathematics and Statistics, Southern Illinois University Edwardsville/Edwardsville, IL 62026-1653/Etats-Unis (2 aut.)</AF>
<DT>Publication en série; Niveau analytique</DT>
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<LA>Anglais</LA>
<EA>While a number of researchers have previously investigated the relationship between graph theory and quantum probability, the current work explores a new perspective. The approach of this paper is to begin with an arbitrary graph having no previously established relationship to quantum probability and to use that graph to construct a quantum probability space in which moments of quantum random variables reveal information about the graph's structure. Given an arbitrary finite graph and arbitrary odd integer m≥ 3, fermion annihilation operators are used to construct a family of quantum random variables whose mth moments correspond to the graph's m-cycles. The approach is then generalized to recover a graph's m-cycles for any integer m≥ 3 by defining nilpotent adjacency operators in terms of null-square generators of an infinite-dimensional Abelian algebra. It is shown that ordering the vertices of a simple graph induces a canonical decompositionΨ =Ψ<sup>+</sup>
 + Ψ<sup>-</sup>
 on any nilpotent adjacency operator Ψ. The work concludes with applications to Markov chains and random graphs.</EA>
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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

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