Spectral Analysis of Growing Graphs

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Beschreibung

This book is designed as a concise introduction to the recent achievements on spectral analysis of graphs or networks from the point of view of quantum (or non-commutative) probability theory. The main topics are spectral distributions of the adjacency matrices of finite or infinite graphs and their limit distributions for growing graphs. The main vehicle is quantum probability, an algebraic extension of the traditional probability theory, which provides a new framework for the analysis of adjacency matrices revealing their non-commutative nature. For example, the method of quantum decomposition makes it possible to study spectral distributions by means of interacting Fock spaces or equivalently by orthogonal polynomials. Various concepts of independence in quantum probability and corresponding central limit theorems are used for the asymptotic study of spectral distributions for product graphs.

This book is written for researchers, teachers, and students interested in graph spectra, their (asymptotic) spectral distributions, and various ideas and methods on the basis of quantum probability. It is also useful for a quick introduction to quantum probability and for an analytic basis of orthogonal polynomials.

Zusammenfassung

Presents a concise introduction to quantum probability theory as a unique tool for analyzing graph spectra and their asymptotics

Comprises a unique textbook showing the interplay of quantum probability and spectral graph theory

Contains exercises with brief guides to solutions

Includes supplementary material: [...]

Inhaltsverzeichnis

1. Graphs and Matrices.- 2. Spectra of Finite Graphs.- 3. Spectral Distributions of Graphs.- 4. Orthogonal Polynomials and Fock Spaces.- 5. Analytic Theory of Moments.- 6. Method of Quantum Decomposition.- 7. Graph Products and Asymptotics.- References.- Index.

Details

Erscheinungsjahr:	2017
Fachbereich:	Allgemeines
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	viii 138 S. 13 s/w Illustr. 9 farbige Illustr. 138 p. 22 illus. 9 illus. in color.
ISBN-13:	9789811035050
ISBN-10:	9811035059
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Obata, Nobuaki
Auflage:	2017 edition
Hersteller:	Springer Singapore Springer Nature Singapore
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	236 x 154 x 12 mm
Von/Mit:	Nobuaki Obata
Erscheinungsdatum:	23.02.2017
Gewicht:	0,248 kg

Artikel-ID: 108497340