### 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 language | English |
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Pages (from-to) | 419-435 |

Number of pages | 17 |

Journal | Infinite Dimensional Analysis, Quantum Probability and Related Topics |

Volume | 7 |

Issue number | 3 |

DOIs | |

Publication status | Published - 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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## Cite this

Accardi, L., Ghorbal, A. B., & Obata, N. (2004). Monotone independence, comb graphs and bose-einstein condensation.

*Infinite Dimensional Analysis, Quantum Probability and Related Topics*,*7*(3), 419-435. https://doi.org/10.1142/S0219025704001645