Circuits in random graphs: From local trees to global loops

Enzo Marinari; Rémi Monasson

doi:10.1088/1742-5468/2004/09/P09004

Circuits in random graphs: From local trees to global loops

Enzo Marinari
, Rémi Monasson

Dipartimento di Fisica
Center for Atomic-scale Materials Physics (CAMP)

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We compute the number of circuits and of loops with multiple crossings in random regular graphs. We discuss the importance of this issue for the validity of the cavity approach. On the one hand we obtain analytical results for the infinite volume limit in agreement with existing exact results. On the other hand we implement a counting algorithm, enumerate circuits at finite N, and draw some general conclusions about the finite-N behaviour of the number of circuits.

langue originale	Anglais
Numéro d'article	P09004
journal	Journal of Statistical Mechanics: Theory and Experiment
Numéro de publication	9
Les DOIs	https://doi.org/10.1088/1742-5468/2004/09/P09004
état	Publié - 1 janv. 2004
Modification externe	Oui

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10.1088/1742-5468/2004/09/P09004

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title = "Circuits in random graphs: From local trees to global loops",

abstract = "We compute the number of circuits and of loops with multiple crossings in random regular graphs. We discuss the importance of this issue for the validity of the cavity approach. On the one hand we obtain analytical results for the infinite volume limit in agreement with existing exact results. On the other hand we implement a counting algorithm, enumerate circuits at finite N, and draw some general conclusions about the finite-N behaviour of the number of circuits.",

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AB - We compute the number of circuits and of loops with multiple crossings in random regular graphs. We discuss the importance of this issue for the validity of the cavity approach. On the one hand we obtain analytical results for the infinite volume limit in agreement with existing exact results. On the other hand we implement a counting algorithm, enumerate circuits at finite N, and draw some general conclusions about the finite-N behaviour of the number of circuits.

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KW - spin glasses (theory)

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Circuits in random graphs: From local trees to global loops

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