Monotone independence, comb graphs and bose-einstein condensation

Luigi Accardi, Anis Ben Ghorbal, Nobuaki Obata

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

The adjacency matrix of a comb graph is decomposed into a sum of monotone independent random variables with respect to the vacuum state. The vacuum spectral distribution is shown to be asymptotically the arcsine law as a consequence of the monotone central limit theorem. As an example the comb lattice is studied with explicit calculation.

Original languageEnglish
Pages (from-to)419-435
Number of pages17
JournalInfinite Dimensional Analysis, Quantum Probability and Related Topics
Volume7
Issue number3
DOIs
Publication statusPublished - 2004 Sep

Keywords

  • Adjacency matrix
  • Comb graph
  • Interacting Fock space
  • Monotone independence
  • Quantum decomposition
  • Semicircle law
  • Spectral distribution

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Mathematical Physics
  • Applied Mathematics

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