Information-theoretic thresholds from the cavity method

Abstract : Vindicating a sophisticated but non-rigorous physics approach called the cavity method, we establish a formula for the mutual information in statistical inference problems induced by random graphs and we show that the mutual information holds the key to understanding certain important phase transitions in random graph models. We work out several concrete applications of these general results. For instance, we pinpoint the exact condensation phase transition in the Potts antiferromagnet on the random graph, thereby improving prior approximate results [Contucci et al.: Communications in Mathematical Physics 2013]. Further, we prove the conjecture from [Krzakala et al.: PNAS 2007] about the condensation phase transition in the random graph coloring problem for any number q ≥ 3 of colors. Moreover , we prove the conjecture on the information-theoretic threshold in the disassortative stochastic block model [Decelle et al.: Phys. Rev. E 2011]. Additionally, our general result implies the conjectured formula for the mutual information in Low-Density Generator Matrix codes [Montanari: IEEE Transactions on Information Theory 2005].
Liste complète des métadonnées

Littérature citée [86 références]  Voir  Masquer  Télécharger
Contributeur : Emmanuelle De Laborderie <>
Soumis le : vendredi 27 janvier 2017 - 14:55:50
Dernière modification le : vendredi 4 janvier 2019 - 17:32:25
Document(s) archivé(s) le : samedi 29 avril 2017 - 01:20:21


Fichiers produits par l'(les) auteur(s)


  • HAL Id : cea-01448087, version 1
  • ARXIV : 1611.00814


Amin Coja-Oghlan, Florent Krzakala, Will Perkins, Lenka Zdeborova. Information-theoretic thresholds from the cavity method. 2017. 〈cea-01448087〉



Consultations de la notice


Téléchargements de fichiers