© 2007

Quantum Probability and Spectral Analysis of Graphs


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


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.


Graph Theory Quantum Probability Spectral Analysis algebra calculus orthogonal polynomials

Authors and affiliations

  1. 1.Graduate School of MathematicsNagoya UniverstiyNagoyaJapan
  2. 2.Graduate School of Information SciencesTohoku UniversitySendaiJapan

About the authors

Quantum Probability and Orthogonal Polynomials.- Adjacency Matrix.- Distance-Regular Graph.- Homogeneous Tree.- Hamming Graph.- Johnson Graph.- Regular Graph.- Comb Graph and Star Graph.- Symmetric Group and Young Diagram.- Limit Shape of Young Diagrams.- Central Limit Theorem for the Plancherel Measure of the Symmetric Group.- Deformation of Kerov's Central Limit Theorem.- References.- Index.

Bibliographic information

Industry Sectors
Energy, Utilities & Environment


From the reviews:

"It is a very accessible introduction for the non expert to a few rapidly evolving areas of mathematics such as spectral analysis of graphs … . this monograph seems to be the first publication providing a synthesis of a very vast mathematical literature in these areas by giving to the reader a concise and self contained panorama of existing results … . this book is important to the quantum probability community and emphasizes well many new applications of quantum probability to other areas of mathematics." (Benoit Collins, Zentralblatt MATH, Vol. 1141, 2008)