Theoretical and Mathematical Physics

Quantum Probability and Spectral Analysis of Graphs

Authors: Hora, Akihito, Obata, Nobuaki

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  • Presents an approach to spectral analysis of graphs that was developed by the authors.
  • Introduces quantum probability from an algebraic perspective.
  • Includes end-of-chapter exercises to reinforce understanding.
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eBook $119.00
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  • ISBN 978-3-540-48863-7
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Hardcover $159.00
price for USA in USD
  • ISBN 978-3-540-48862-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.99
price for USA in USD
  • ISBN 978-3-642-08026-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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.

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.

Reviews

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)


Table of contents (12 chapters)

Table of contents (12 chapters)
  • Quantum Probability and Orthogonal Polynomials

    Hora, Professor Akihito, Dr. (et al.)

    Pages 1-63

  • Adjacency Matrices

    Hora, Professor Akihito, Dr. (et al.)

    Pages 65-83

  • Distance-Regular Graphs

    Hora, Professor Akihito, Dr. (et al.)

    Pages 85-103

  • Homogeneous Trees

    Hora, Professor Akihito, Dr. (et al.)

    Pages 105-130

  • Hamming Graphs

    Hora, Professor Akihito, Dr. (et al.)

    Pages 131-146

Buy this book

eBook $119.00
price for USA in USD (gross)
  • ISBN 978-3-540-48863-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.00
price for USA in USD
  • ISBN 978-3-540-48862-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.99
price for USA in USD
  • ISBN 978-3-642-08026-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Quantum Probability and Spectral Analysis of Graphs
Authors
Series Title
Theoretical and Mathematical Physics
Copyright
2007
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-48863-7
DOI
10.1007/3-540-48863-4
Hardcover ISBN
978-3-540-48862-0
Softcover ISBN
978-3-642-08026-5
Series ISSN
1864-5879
Edition Number
1
Number of Pages
XVIII, 371
Number of Illustrations
8 b/w illustrations
Topics