Akihito Hora, Nobuaki Obata

eBook, PDF

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

Beschreibung

This is the first book to comprehensively cover quantum probabilistic approach to spectral analysis of graphs. This approach was initiated by the authors and has become an interesting research area in applied mathematics and physics. The text offers a concise introduction to quantum probability from an algebraic perspective. Topics discussed along the way include quantum probability and orthogonal polynomials, asymptotic spectral theory (quantum central limit theorems) for adjacency matrices, method of quantum decomposition, notions of independence and structure of graphs, and asymptotic representation theory of the symmetric groups. Readers will learn several powerful methods and techniques of wide applicability, recently developed under the name of quantum probability. End-of-chapter exercises promote deeper understanding.

Technische Details

• Geräte: PC
• ohne Kopierschutz
• Größe: 3.88MB

Barrierefreiheit

• Text-to-Speech

Autor

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.

Produktdetails

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

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)