InforLorV4, PascalFrancis, Checkpoint, bibRecord, 000272

Nilpotent adjacency matrices, random graphs and quantum random variables

Identifieur interne : 000272 ( PascalFrancis/Checkpoint ); précédent : 000271; suivant : 000273

Nilpotent adjacency matrices, random graphs and quantum random variables

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

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.

Affiliations:

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Pascal:08-0216287

Le document en format XML

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<front><div type="abstract" xml:lang="en">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>
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Nilpotent adjacency matrices, random graphs and quantum random variables

Nilpotent adjacency matrices, random graphs and quantum random variables

Source :

Descripteurs français

English descriptors

Abstract

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

Links to Exploration step

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

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