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Spectral Analysis of Growing Graphs

A Quantum Probability Point of View

  • Book
  • © 2017

Overview

Authors:
  1. Nobuaki Obata

    1. Graduate School of Information Sciences, Tohoku University, Sendai, Japan

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  • 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: sn.pub/extras

Part of the book series: SpringerBriefs in Mathematical Physics (BRIEFSMAPHY, volume 20)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-viii
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  2. Graphs and Matrices

    • Nobuaki Obata
    Pages 1-15

  3. Spectra of Finite Graphs

    • Nobuaki Obata
    Pages 17-29

  4. Spectral Distributions of Graphs

    • Nobuaki Obata
    Pages 31-41

  5. Orthogonal Polynomials and Fock Spaces

    • Nobuaki Obata
    Pages 43-61

  6. Analytic Theory of Moments

    • Nobuaki Obata
    Pages 63-77

  7. Method of Quantum Decomposition

    • Nobuaki Obata
    Pages 79-99

  8. Graph Products and Asymptotics

    • Nobuaki Obata
    Pages 101-128

  9. Back Matter

    Pages 129-138
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Keywords

About this book

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.

Authors and Affiliations

  • Graduate School of Information Sciences, Tohoku University, Sendai, Japan

    Nobuaki Obata

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