Asymptotic spectral analysis of growing regular graphs

Akihito Hora; Nobuaki Obata

doi:10.1090/S0002-9947-07-04232-8

Asymptotic spectral analysis of growing regular graphs

Akihito Hora, Nobuaki Obata

INF - System Information Sciences

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

We propose the quantum probabilistic techniques to ob tain the asymptotic spectral distribution of the adjacency matrix of a growing regular graph. We prove the quantum central limit theorem for the adjacency matrix of a growing regular graph in the vacuum and deformed vacuum states. The condition for the growth is described in terms of simple statistics arising from the stratification of the graph. The asymptotic spectral distribution of the adjacency matrix is obtained from the classical reduction.

Original language	English
Pages (from-to)	899-923
Number of pages	25
Journal	Transactions of the American Mathematical Society
Volume	360
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9947-07-04232-8
Publication status	Published - 2008 Feb

Keywords

Adjacency matrix
Interacting fock space
Orthogonal polynomial
Quantum central limit theorem
Quantum decomposition
Spectral distribution

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9947-07-04232-8

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AB - We propose the quantum probabilistic techniques to ob tain the asymptotic spectral distribution of the adjacency matrix of a growing regular graph. We prove the quantum central limit theorem for the adjacency matrix of a growing regular graph in the vacuum and deformed vacuum states. The condition for the growth is described in terms of simple statistics arising from the stratification of the graph. The asymptotic spectral distribution of the adjacency matrix is obtained from the classical reduction.

KW - Adjacency matrix

KW - Interacting fock space

KW - Orthogonal polynomial

KW - Quantum central limit theorem

KW - Quantum decomposition

KW - Spectral distribution

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

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Asymptotic spectral analysis of growing regular graphs

Abstract

Keywords

ASJC Scopus subject areas

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