
Spectral Analysis of Growing Graphs
A Quantum Probability Point of View
Nobuaki Obata(Author)
Springer (Publisher)
Published on 23. February 2017
Book
Paperback/Softback
VIII, 138 pages
978-981-10-3505-0 (ISBN)
Description
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.
More details
Series
Edition
2017
Language
English
Place of publication
Singapore
Singapore
Target group
Professional and scholarly
Product notice
Paperback (trade)
Unsewn / adhesive bound
Illustrations
13 s/w Abbildungen, 9 farbige Abbildungen
VIII, 138 p. 22 illus., 9 illus. in color.
Dimensions
Height: 236 mm
Width: 154 mm
Thickness: 12 mm
Weight
248 gr
ISBN-13
978-981-10-3505-0 (9789811035050)
DOI
10.1007/978-981-10-3506-7
Schweitzer Classification
Other editions
Additional editions

E-Book
02/2017
Springer
€74.89
Available for download
Content
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.