Sinossi
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.
Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.
Informazioni sull?autore
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.
Dalla quarta di copertina
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.
Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.
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Quantum Probability and Spectral Analysis of Graphs (Theoretical and Mathematical Physics)
Editore:
Springer, 2007
ISBN 10: 3540488626
ISBN 13: 9783540488620
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Da: killarneybooks, Inagh, CLARE, Irlanda
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Hardcover. Condizione: Near Fine. 1st Edition. Hardcover, xviii+371 pages, NOT ex-library. Clean and bright throughout, unmarked text, no inscriptions/stamps, firmly bound. Minor shelfwear. -- An integration of quantum probability theory with spectral graph analysis, developing a powerful algebraic framework to investigate the asymptotic spectral behavior of large and growing graphs. This monograph builds upon von Neumann's foundational ideas, redefining random variables and measures in terms of self-adjoint operators and traces, and extends them into a structured analytic approach that reveals how quantum probabilistic tools can resolve longstanding questions in graph theory, operator algebras and mathematical physics. The core innovation is the method of quantum decomposition, which translates classical probability distributions into the language of interacting Fock spaces using orthogonal polynomials and three-term recurrence relations. By treating adjacency matrices as algebraic random variables, the authors develop a comprehensive method to derive spectral distributions and their limits in infinite graph sequences. This approach yields a unified framework in which quantum central limit theorems QCLTs take center stage, providing exact descriptions of asymptotic spectral distributions across families of distance-regular graphs. Chapters 1 & 2 establish foundational concepts in algebraic and quantum probability, including moment problems, Stieltjes transforms and Fock space constructions, before introducing the adjacency matrix as a noncommutative observable. The method is then applied across multiple graph classes. In homogeneous trees, the Wigner semicircle law and free Poisson distribution emerge naturally; in Hamming and Johnson graphs, Gaussian, exponential, geometric and Poisson limits are derived. Odd graphs lead to the two-sided Rayleigh distribution, demonstrating the framework's range. These results bridge classical and free probability in a concrete setting, offering a systematic toolkit for analyzing complex graph spectra. The book's discussion of quantum notions of independence (tensor, free, Boolean, monotone) is significant. By modeling these through graph operations such as the comb and star products, the authors provide new perspectives on the underlying algebraic structures and also practical methods for constructing graph models associated with different statistical behaviors. This graphical realization of independence deepens the connection between quantum probability and graph theory and sets the stage for novel applications in network science, random matrix theory and high-dimensional combinatorics. Chapters 9-12 pivot to the asymptotic representation theory of symmetric groups, using the tools developed to study Young diagrams under the Plancherel and Jack measures. The book offers a fresh derivation of the limit shape and Gaussian fluctuations in the Plancherel setting, connecting the spectral properties of adjacency matrices with Kerov's central limit theorem and its deformations. The authors also analyze the alpha-deformation via the Jack measure and demonstrate its implications for the Metropolis algorithm, revealing the practical relevance of their method in probabilistic sampling and statistical mechanics. By blending abstract algebraic constructions with detailed worked examples and asymptotic results, this volume addresses a broad range of contemporary mathematical problems. It contributes to ongoing discussions in noncommutative probability, spectral asymptotics, graph growth models and the analytic structure of symmetric group representations. Its accessible treatment makes it valuable for mathematicians and theoretical physicists working in quantum information, large-scale network analysis, random walks on groups or noncommutative harmonic analysis. It opens new avenues for applying quantum probabilistic methods to data science, particularly in contexts where complex network structures demand tools beyond classical probabilistic models. Codice articolo 011333
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Quantum Probability and Spectral Analysis of Graphs (Theoretical and Mathematical Physics)
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Quantum Probability and Spectral Analysis of Graphs
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Springer Berlin Heidelberg Mai 2007, 2007
ISBN 10: 3540488626
ISBN 13: 9783540488620
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Da: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germania
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Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 396 pp. Englisch. Codice articolo 9783540488620
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Quantum Probability and Spectral Analysis of Graphs
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Gebunden. Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. This is the first monograph written on the quantum probability approach to spectral analysis of graphs, a subject initiated by the authors many years agoQuantum Probability and Orthogonal Polynomials.- Adjacency Matrix.- Distance-Regular Graph.- Homogen. Codice articolo 4891302
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Quantum Probability and Spectral Analysis of Graphs
Da: Books Puddle, New York, NY, U.S.A.
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Condizione: New. pp. 396. Codice articolo 26302238
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Quantum Probability and Spectral Analysis of Graphs
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Condizione: New. Print on Demand pp. 396 Illus. Codice articolo 7545665
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Quantum Probability and Spectral Analysis of Graphs
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Condizione: New. PRINT ON DEMAND pp. 396. Codice articolo 18302228
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Quantum Probability and Spectral Analysis of Graphs
Editore:
Springer, Springer Mai 2007, 2007
ISBN 10: 3540488626
ISBN 13: 9783540488620
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Da: buchversandmimpf2000, Emtmannsberg, BAYE, Germania
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Buch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 396 pp. Englisch. Codice articolo 9783540488620
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Quantum Probability and Spectral Analysis of Graphs
Da: Revaluation Books, Exeter, Regno Unito
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Hardcover. Condizione: Brand New. 1st edition. 371 pages. 9.50x6.50x0.75 inches. In Stock. Codice articolo x-3540488626
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Quantum Probability and Spectral Analysis of Graphs (Theoretical and Mathematical Physics)
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hardcover. Condizione: New. In shrink wrap. Looks like an interesting title! Codice articolo Q-3540488626
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