Spectral Analysis of Growing Graphs: A Quantum Probability Point of View

Front Cover
Springer, Feb 17, 2017 - Science - 138 pages
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.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

1 Graphs and Matrices
1
2 Spectra of Finite Graphs
17
3 Spectral Distributions of Graphs
30
4 Orthogonal Polynomials and Fock Spaces
43
5 Analytic Theory of Moments
62
6 Method of Quantum Decomposition
79
7 Graph Products and Asymptotics
101
References
129
Index
135
Copyright

Other editions - View all

Common terms and phrases

Bibliographic information