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.
Accardi, L., Ben Ghorbal, A., Obata, N. (2004). Monotone independence, comb graphs and Bose-Einstein condensation. INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 7(3), 419-435 [10.1142/S0219025704001645].
Monotone independence, comb graphs and Bose-Einstein condensation
ACCARDI, LUIGI;
2004-01-01
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.File in questo prodotto:
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