# 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.
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Cited literature [19 references]

https://hal.archives-ouvertes.fr/hal-00983930
Contributor : Justin Salez <>
Submitted on : Saturday, April 26, 2014 - 11:09:56 AM
Last modification on : Friday, March 27, 2020 - 3:58:44 AM
Document(s) archivé(s) le : Saturday, July 26, 2014 - 10:45:56 AM

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### Identifiers

• 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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