Quantum Probability and Spectral Analysis of Graphs - Brossura

Hora, Akihito; Obata, Nobuaki

Brossura

ISBN 10: 364208026X ISBN 13: 9783642080265

Casa editrice: Springer, 2010

Riassunto

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.

Su questo libro

Informazioni sull?autore

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.

Dalla quarta di copertina

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.

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 364208026X
• ISBN 13: 9783642080265
• Rilegatura: Copertina flessibile
• Numero di pagine: 392
• Contatto del produttore: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Germania