Quantum Probability and Spectral Analysis of Graphs [Hardcover]

This is the first book to comprehensively cover quantum probabilistic approaches to spectral analysis of graphs, an approach developed by the authors. The book functions as a concise introduction to quantum probability from an algebraic aspect. Here readers will learn several powerful methods and techniques of wide applicability, recently developed under the name of quantum probability. The exercises at the end of each chapter help to deepen understanding.

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, Nevanlinnastheoryandthetheoryofrepresentationsofthesymmetricgroup. 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 establil,