Overview
- Authors:
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Akihito Hora
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Graduate School of Mathematics, Nagoya Universtiy, Nagoya, Japan
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Nobuaki Obata
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Graduate School of Information Sciences, Tohoku University, Sendai, Japan
- This is the first monograph written on the quantum probability approach to spectral analysis of graphs, a subject initiated by the authors many years ago
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Table of contents (12 chapters)
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Front Matter
Pages I-XVIII
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- Akihito Hora, Nobuaki Obata
Pages 1-63
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- Akihito Hora, Nobuaki Obata
Pages 65-83
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- Akihito Hora, Nobuaki Obata
Pages 85-103
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- Akihito Hora, Nobuaki Obata
Pages 105-130
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- Akihito Hora, Nobuaki Obata
Pages 131-146
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- Akihito Hora, Nobuaki Obata
Pages 147-173
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- Akihito Hora, Nobuaki Obata
Pages 175-203
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- Akihito Hora, Nobuaki Obata
Pages 205-247
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- Akihito Hora, Nobuaki Obata
Pages 249-270
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- Akihito Hora, Nobuaki Obata
Pages 271-296
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- Akihito Hora, Nobuaki Obata
Pages 297-320
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- Akihito Hora, Nobuaki Obata
Pages 321-350
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Back Matter
Pages 351-373
About this book
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.
Reviews
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)
Authors and Affiliations
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Graduate School of Mathematics, Nagoya Universtiy, Nagoya, Japan
Akihito Hora
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Graduate School of Information Sciences, Tohoku University, Sendai, Japan
Nobuaki Obata
About the authors
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.
