# The interpolation method for random graphs with prescribed degrees

1 Modélisation stochastique
LPMA - Laboratoire de Probabilités et Modèles Aléatoires
Abstract : We consider large random graphs with prescribed degrees, such as those generated by the configuration model. In the regime where the empirical degree distribution approaches a limit $\mu$ with finite mean, we establish the systematic convergence of a broad class of graph parameters that includes in particular the independence number, the maximum cut size and the log-partition function of the antiferromagnetic Ising and Potts models. The corresponding limits are shown to be Lipschitz and concave functions of $\mu$. Our work extends the applicability of the celebrated interpolation method, introduced in the context of spin glasses, and recently related to the fascinating problem of right-convergence of sparse graphs.
Keywords :
Type de document :
Pré-publication, Document de travail
2014
Domaine :

https://hal.archives-ouvertes.fr/hal-00983930
Contributeur : Justin Salez <>
Soumis le : samedi 26 avril 2014 - 11:09:56
Dernière modification le : lundi 29 mai 2017 - 14:25:55
Document(s) archivé(s) le : samedi 26 juillet 2014 - 10:45:56

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draft.pdf
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### Identifiants

• HAL Id : hal-00983930, version 1
• ARXIV : 1404.6647

### Citation

Justin Salez. The interpolation method for random graphs with prescribed degrees. 2014. <hal-00983930>

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