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Properties of Atypical Graphs from Negative Complexities

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Abstract

The one-step replica symmetry breaking cavity method is proposed as a new tool to investigate large deviations in random graph ensembles. The procedure hinges on a general connection between negative complexities and probabilities of rare samples in spin glass like models. This relation between large deviations and replica theory is explicited on different models where it is confronted to direct combinatorial calculations.

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  1. Laboratoire de Physique Théorique et Modèles Statistiques bât. 100, Université, Paris-Sud, France

    Olivier Rivoire

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  1. Olivier Rivoire
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Rivoire, O. Properties of Atypical Graphs from Negative Complexities. Journal of Statistical Physics 117, 453–476 (2004). https://doi.org/10.1007/s10955-004-2265-9

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  • DOI: https://doi.org/10.1007/s10955-004-2265-9

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