Quantum Probability and Spectral Analysis of Graphs

  • Akihito Hora
  • Nobuaki Obata

Part of the Theoretical and Mathematical Physics book series (TMP)

Table of contents

  1. Front Matter
    Pages I-XVIII
  2. Akihito Hora, Nobuaki Obata
    Pages 1-63
  3. Akihito Hora, Nobuaki Obata
    Pages 65-83
  4. Akihito Hora, Nobuaki Obata
    Pages 85-103
  5. Akihito Hora, Nobuaki Obata
    Pages 105-130
  6. Akihito Hora, Nobuaki Obata
    Pages 131-146
  7. Akihito Hora, Nobuaki Obata
    Pages 147-173
  8. Akihito Hora, Nobuaki Obata
    Pages 175-203
  9. Akihito Hora, Nobuaki Obata
    Pages 205-247
  10. Akihito Hora, Nobuaki Obata
    Pages 249-270
  11. Akihito Hora, Nobuaki Obata
    Pages 271-296
  12. Akihito Hora, Nobuaki Obata
    Pages 321-350
  13. Back Matter
    Pages 351-373

About this book

Introduction

This is the first book to comprehensively cover the quantum probabilistic approach to spectral analysis of graphs. This approach has been developed by the authors and has become an interesting research area in applied mathematics and physics. The book can be used as a concise introduction to quantum probability from an algebraic aspect. Here readers will learn several powerful methods and techniques of wide applicability, which have been recently developed under the name of quantum probability. The exercises at the end of each chapter help to deepen understanding.

Among the topics discussed along the way are: quantum probability and orthogonal polynomials; asymptotic spectral theory (quantum central limit theorems) for adjacency matrices; the method of quantum decomposition; notions of independence and structure of graphs; and asymptotic representation theory of the symmetric groups.

Keywords

Graph Theory Quantum Probability Spectral Analysis algebra calculus orthogonal polynomials

Authors and affiliations

  • Akihito Hora
    • 1
  • Nobuaki Obata
    • 2
  1. 1.Graduate School of MathematicsNagoya UniverstiyNagoyaJapan
  2. 2.Graduate School of Information SciencesTohoku UniversitySendaiJapan

Bibliographic information

  • DOI https://doi.org/10.1007/3-540-48863-4
  • Copyright Information Springer 2007
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-540-48862-0
  • Online ISBN 978-3-540-48863-7
  • Series Print ISSN 0172-5998
  • About this book