Asymptotic spectral analysis of growing regular graphs

Akihito Hora, Nobuaki Obata

Research output: Contribution to journalArticle

6 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 languageEnglish
Pages (from-to)899-923
Number of pages25
JournalTransactions of the American Mathematical Society
Volume360
Issue number2
DOIs
Publication statusPublished - 2008 Feb 1

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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