Quantum Probability and Spectral Analysis of Graphs (Theoretical and Mathematical Physics) - Hardcover

Hora, Akihito; Obata, Nobuaki

Hardcover

ISBN 10: 3540488626 ISBN 13: 9783540488620

Verlag: Springer, 2007

Inhaltsangabe

It is a great pleasure for me that the new Springer Quantum Probability ProgrammeisopenedbythepresentmonographofAkihitoHoraandNobuaki Obata. In fact this book epitomizes several distinctive features of contemporary quantum probability: First of all the use of speci?c quantum probabilistic techniques to bring original and quite non-trivial contributions to problems with an old history and on which a huge literature exists, both independent of quantum probability. Second, but not less important, the ability to create several bridges among di?erent branches of mathematics apparently far from one another such as the theory of orthogonal polynomials and graph theory, Nevanlinna’stheoryandthetheoryofrepresentationsofthesymmetricgroup. Moreover, the main topic of the present monograph, the asymptotic - haviour of large graphs, is acquiring a growing importance in a multiplicity of applications to several di?erent ?elds, from solid state physics to complex networks,frombiologytotelecommunicationsandoperationresearch,toc- binatorialoptimization.Thiscreatesapotentialaudienceforthepresentbook which goes far beyond the mathematicians and includes physicists, engineers of several di?erent branches, as well as biologists and economists. From the mathematical point of view, the use of sophisticated analytical toolstodrawconclusionsondiscretestructures,suchas,graphs,isparticularly appealing. The use of analysis, the science of the continuum, to discover n- trivial properties of discrete structures has an established tradition in number theory, but in graph theory it constitutes a relatively recent trend and there are few doubts that this trend will expand to an extent comparable to what we ?nd in the theory of numbers. Two main ideas of quantum probability form theunifying framework of the present book: 1. The quantum decomposition of a classical random variable.

Über diesen Titel

Über die Autorin bzw. den 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.

Von der hinteren Coverseite

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.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2007
• Sprache: Englisch
• ISBN 10: 3540488626
• ISBN 13: 9783540488620
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 389
• Kontakt zum Hersteller: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Tiergartenstr. 17; Heidelberg; 69121; Deutschland