Exponential extinction time of the contact process on finite graphs

Abstract : We study the extinction time τ of the contact process started with full occupancy on finite trees of bounded degree. We show that, if the infection rate is larger than the critical rate for the contact process on Z, then, uniformly over all trees of degree bounded by a given number, the expectation of τ grows exponentially with the number of vertices. Additionally, for any increasing sequence of trees of bounded degree, τ divided by its expectation converges in distribution to the unitary exponential distribution. These results also hold if one considers a sequence of graphs having spanning trees with uniformly bounded degree, and provide the basis for powerful coarse-graining arguments. To demonstrate this, we consider the contact process on a random graph with vertex degrees following a power law. Improving a result of Chatterjee and Durrett [CD09], we show that, for any non-zero infection rate, the extinction time for the contact process on this graph grows exponentially with the number of vertices.
Type de document :
Article dans une revue
Stochastic Processes and their Applications, Elsevier, 2016, 126, pp.1974 - 2013. 〈10.1016/j.spa.2016.01.001〉
Liste complète des métadonnées

https://hal-ens-lyon.archives-ouvertes.fr/ensl-01401886
Contributeur : Jean-Christophe Mourrat <>
Soumis le : mercredi 23 novembre 2016 - 22:21:10
Dernière modification le : jeudi 11 janvier 2018 - 06:12:31

Fichiers

contactexp.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Thomas Mountford, Jean-Christophe Mourrat, Daniel Valesin, Qiang Yao. Exponential extinction time of the contact process on finite graphs. Stochastic Processes and their Applications, Elsevier, 2016, 126, pp.1974 - 2013. 〈10.1016/j.spa.2016.01.001〉. 〈ensl-01401886〉

Partager

Métriques

Consultations de la notice

24

Téléchargements de fichiers

47