Central limit theorems for large graphs: Method of quantum decomposition

Yukihiro Hashimoto, Akihito Hora, Nobuaki Obata

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

A new method is proposed for investigating spectral distribution of the combinatorial Laplacian (adjacency matrix) of a large regular graph on the basis of quantum decomposition and quantum central limit theorem. General results are proved for Cayley graphs of discrete groups and for distance-regular graphs. The Coxeter groups and the Johnson graphs are discussed in detail by way of illustration. In particular, the limit distributions obtained from the Johnson graphs are characterized by the Meixner polynomials which form a one-parameter deformation of the Laguerre polynomials.

Original languageEnglish
Pages (from-to)71-88
Number of pages18
JournalJournal of Mathematical Physics
Volume44
Issue number1
DOIs
Publication statusPublished - 2003 Jan 1

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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