Rigorous Result for the CHKNS Random Graph Model

Abstract : We study the phase transition in a random graph in which vertices and edges are added at constant rates. Two recent papers in Physical Review E by Callaway, Hopcroft, Kleinberg, Newman, and Strogatz, and Dorogovstev, Mendes, and Samukhin have computed the critical value of this model, shown that the fraction of vertices in finite clusters is infinitely differentiable at the critical value, and that in the subcritical phase the cluster size distribution has a polynomial decay rate with a continuously varying power. Here we sketch rigorous proofs for the first and third results and a new estimates about connectivity probabilities at the critical value.
Type de document :
Communication dans un congrès
Cyril Banderier and Christian Krattenthaler. Discrete Random Walks, DRW'03, 2003, Paris, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03), pp.95-104, 2003, DMTCS Proceedings
Liste complète des métadonnées

Littérature citée [15 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-01183940
Contributeur : Coordination Episciences Iam <>
Soumis le : mercredi 12 août 2015 - 09:08:24
Dernière modification le : mardi 24 avril 2018 - 17:20:13
Document(s) archivé(s) le : vendredi 13 novembre 2015 - 11:38:14

Fichier

dmAC0109.pdf
Fichiers éditeurs autorisés sur une archive ouverte

Identifiants

  • HAL Id : hal-01183940, version 1

Collections

Citation

Rick Durrett. Rigorous Result for the CHKNS Random Graph Model. Cyril Banderier and Christian Krattenthaler. Discrete Random Walks, DRW'03, 2003, Paris, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03), pp.95-104, 2003, DMTCS Proceedings. 〈hal-01183940〉

Partager

Métriques

Consultations de la notice

181

Téléchargements de fichiers

177