Quantum Probability and Spectral Analysis of Graphs
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 specific 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 different branches of mathematics apparently far from one another such as the theory of orthogonal polynomials and graph theory, Nevanlinna’stheoryandthetheoryofrepresentationsof thesymmetricgroup. 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 different fields, from solid state physics to complex networks,frombiologytotelecommunicationsandoperationresearch,- binatorialoptimization.Thiscreatesapotentialaudienceforthepresentbook which goes far beyond the mathematicians and includes physicists, engineers of several different 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 find 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.
1101668480
Quantum Probability and Spectral Analysis of Graphs
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 specific 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 different branches of mathematics apparently far from one another such as the theory of orthogonal polynomials and graph theory, Nevanlinna’stheoryandthetheoryofrepresentationsof thesymmetricgroup. 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 different fields, from solid state physics to complex networks,frombiologytotelecommunicationsandoperationresearch,- binatorialoptimization.Thiscreatesapotentialaudienceforthepresentbook which goes far beyond the mathematicians and includes physicists, engineers of several different 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 find 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.
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Quantum Probability and Spectral Analysis of Graphs

Quantum Probability and Spectral Analysis of Graphs

Quantum Probability and Spectral Analysis of Graphs

Quantum Probability and Spectral Analysis of Graphs

Overview

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 specific 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 different branches of mathematics apparently far from one another such as the theory of orthogonal polynomials and graph theory, Nevanlinna’stheoryandthetheoryofrepresentationsof thesymmetricgroup. 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 different fields, from solid state physics to complex networks,frombiologytotelecommunicationsandoperationresearch,- binatorialoptimization.Thiscreatesapotentialaudienceforthepresentbook which goes far beyond the mathematicians and includes physicists, engineers of several different 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 find 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.

Product Details

ISBN-13: 9783540488620
Publisher: Springer Berlin Heidelberg
Publication date: 06/11/2007
Series: Theoretical and Mathematical Physics
Edition description: 2007
Pages: 371
Product dimensions: 6.10(w) x 9.25(h) x 0.04(d)

About the Author

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.

Table of Contents

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.
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