Quantum Probability and Spectral Analysis of Graphs

1. Auflage. Softcover version of original hardcover Auflage 2007
ISBN: 978-3-642-08026-5
Verlag: Springer

Buch, Englisch, 371 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 593 g

Reihe: Theoretical and Mathematical Physics

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.

Zielgruppe

Research

Autoren/Hrsg.

Hora, Akihito

Obata, Nobuaki

Weitere Mitwirkende

Accardi, L.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Naturwissenschaften Physik Quantenphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik

Inhaltsverzeichnis

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.

Über Autor(innen)

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.