The contact process on random hyperbolic graphs: metastability and critical exponents - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Annals of Probability Année : 2021

The contact process on random hyperbolic graphs: metastability and critical exponents

Dieter Mitsche
  • Fonction : Auteur
  • PersonId : 949371
Bruno Schapira
  • Fonction : Auteur
  • PersonId : 950892

Résumé

We consider the contact process on the model of hyperbolic random graph, in the regime when the degree distribution obeys a power law with exponent χ ∈ (1, 2) (so that the degree distribution has finite mean and infinite second moment). We show that the probability of non-extinction as the rate of infection goes to zero decays as a power law with an exponent that only depends on χ and which is the same as in the configuration model, suggesting some universality of this critical exponent. We also consider finite versions of the hyperbolic graph and prove metastability results, as the size of the graph goes to infinity.
Fichier principal
Vignette du fichier
CP.hyperbolic-FINAL.pdf (592.34 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Commentaire : Ce pdf est la version preprint de l'article (version soumise à l'éditeur, avant peer-reviewing)
Loading...

Dates et versions

hal-02902848 , version 1 (20-07-2020)

Identifiants

Citer

Amitai Linker, Dieter Mitsche, Bruno Schapira, Daniel Valesin. The contact process on random hyperbolic graphs: metastability and critical exponents. Annals of Probability, 2021, 49 (3), pp.1480-1514. ⟨10.1214/20-AOP1489⟩. ⟨hal-02902848⟩
123 Consultations
35 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More