Strong-majority bootstrap percolation on regular graphs with low dissemination threshold - Laboratoire Jean-Alexandre Dieudonné Accéder directement au contenu
Article Dans Une Revue Stochastic Processes and their Applications Année : 2017

Strong-majority bootstrap percolation on regular graphs with low dissemination threshold

Dieter Mitsche
  • Fonction : Auteur
  • PersonId : 949371
Pawel Pralat
  • Fonction : Auteur

Résumé

Consider the following model of strong-majority bootstrap percolation on a graph. Let r ≥ 1 be some integer, and p ∈ [0, 1]. Initially, every vertex is active with probability p, independently from all other vertices. Then, at every step of the process, each vertex v of degree deg(v) becomes active if at least (deg(v) + r)/2 of its neighbours are active. Given any arbitrarily small p > 0 and any integer r, we construct a family of d = d(p, r)-regular graphs such that with high probability all vertices become active in the end. In particular, the case r = 1 answers a question and disproves a conjecture of Rapaport, Suchan, Todinca and Verstraëte [38].
Fichier principal
Vignette du fichier
bootstrap.pdf (403.6 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02083863 , version 1 (29-03-2019)

Identifiants

  • HAL Id : hal-02083863 , version 1

Citer

Dieter Mitsche, Xavier Pérez-Giménez, Pawel Pralat. Strong-majority bootstrap percolation on regular graphs with low dissemination threshold. Stochastic Processes and their Applications, 2017. ⟨hal-02083863⟩
32 Consultations
60 Téléchargements

Partager

Gmail Facebook X LinkedIn More