Asymptotic spectral analysis of growing regular graphs

DOI10.1090/S0002-9947-07-04232-8zbMath1134.46042MaRDI QIDQ5429477

Nobuaki Obata, Akihito Hora

Publication date: 30 November 2007

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

adjacency matrixspectral distributionorthogonal polynomialquantum central limit theoreminteracting Fock spacequantum decomposition

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Noncommutative probability and statistics (46L53) Quantum stochastic calculus (81S25)

Related Items (6)

Characterizing graphs with fully positive semidefinite \(Q\)-matrices ⋮ Asymptotic joint spectra of Cartesian powers of strongly regular graphs and bivariate Charlier–Hermite polynomials ⋮ Unnamed Item ⋮ TD-pairs and the $q$-Onsager algebra ⋮ ASYMPTOTIC SPECTRAL ANALYSIS OF A GENERALIZED N-CUBE BY A QUANTUM PROBABILISTIC METHOD ⋮ Scaling limits for the Gibbs states on distance-regular graphs with classical parameters

Cites Work

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• Quantum probability and spectral analysis of graphs. With a foreword by Professor Luigi Accardi.
• The expected eigenvalue distribution of a large regular graph
• An example of a non nuclear C*-algebra, which has the metric approximation property
• Representations of symmetric groups and free probability
• Central limit theorem for the adjacency operators on the infinite symmetric group
• Probability on discrete structures
• SCALING LIMIT FOR GIBBS STATES OF JOHNSON GRAPHS AND RESULTING MEIXNER CLASSES
• Asymptotic Spectral Analysis on the Johnson Graphs in Infinite Degree and Zero Temperature Limit
• Quantum Probabilistic Approach to Spectral Analysis of Star Graphs
• Free Random Variables
• Positive-definite kernels, length functions on groups and a noncommutative von Neumann inequality
• Symmetric Random Walks on Groups
• Notions of Independence Related to the Free Group
• Central Limit Theorems and Asymptotic Spectral Analysis on Large Graphs
• Interacting Fock Spaces and Gaussianization of Probability Measures
• QUANTUM DECOMPOSITION IN DISCRETE GROUPS AND INTERACTING FOCK SPACES
• CENTRAL LIMIT THEOREMS FOR COXETER SYSTEMS AND ARTIN SYSTEMS OF EXTRA LARGE TYPE
• Aq-deformed Poisson distribution based on orthogonal polynomials
• MONOTONE INDEPENDENCE, COMB GRAPHS AND BOSE–EINSTEIN CONDENSATION
• Central limit theorems for large graphs: Method of quantum decomposition
• Random Walks on Infinite Graphs and Groups

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