Akihito Hora, Nobuaki Obata

Quantum Probability and Spectral Analysis of Graphs (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 371
• Erscheinungstermin: 5. Juli 2007
• Englisch
• ISBN-13: 9783540488637
• Artikelnr.: 37368401

Autorenporträt

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.

Inhaltsangabe

Quantum Probability and Orthogonal Polynomials.- Adjacency Matrices.- Distance-Regular Graphs.- Homogeneous Trees.- Hamming Graphs.- Johnson Graphs.- Regular Graphs.- Comb Graphs and Star Graphs.- The Symmetric Group and Young Diagrams.- The Limit Shape of Young Diagrams.- Central Limit Theorem for the Plancherel Measures of the Symmetric Groups.- Deformation of Kerov's Central Limit Theorem.

Rezensionen

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)