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MONOTONE INDEPENDENCE, COMB GRAPHS AND BOSE–EINSTEIN CONDENSATION

Università di Roma 2, Via Columbia 2, I-00133 Rome, Italy

Institut für Mathematik und Informatik, Ernst-Moritz-Arndt-Universität Greifswald, Friedrich-Ludwig-Jahn-Straße 15a, D-17487 Greifswald, Germany

Supported by the European Network Training Research "Quantum Probability with Applications to Physics, Information Theory and Biology".

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NOBUAKI OBATA

Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan

Supported in part by the program "R&D support scheme for funding selected IT proposals" of the Ministry of Public Management, Home Affairs, Posts and Telecommunications.

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https://doi.org/10.1142/S0219025704001645Cited by:26 (Source: Crossref)

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.

Keywords:

AMSC: 81S25, 82B20, 05E35, 60F05, 05C50

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