On the non-Gaussian fluctuations of the giant cluster for percolation on random recursive trees - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2013

On the non-Gaussian fluctuations of the giant cluster for percolation on random recursive trees

Jean Bertoin
  • Fonction : Auteur
  • PersonId : 917100

Résumé

We consider a Bernoulli bond percolation on a random recursive tree of size $n\gg 1$, with supercritical parameter $p_n=1-c/\ln n$ for some $c>0$ fixed. It is known that with high probability, there exists then a unique giant cluster of size $G_n\sim \e^{-c}$, and it follows from a recent result of Schweinsberg \cite{Sch} that $G_n$ has non-gaussian fluctuations. We provide an explanation of this by analyzing the effect of percolation on different phases of the growth of recursive trees. This alternative approach may be useful for studying percolation on other classes of trees, such as for instance regular trees.
Fichier principal
Vignette du fichier
Fluctuations_giant.pdf (183.8 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00819320 , version 1 (30-04-2013)
hal-00819320 , version 2 (21-05-2013)

Identifiants

Citer

Jean Bertoin. On the non-Gaussian fluctuations of the giant cluster for percolation on random recursive trees. 2013. ⟨hal-00819320v2⟩
64 Consultations
97 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More