Local limits of galton-watson trees conditioned on the number of protected nodes - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Applied Probability Année : 2017

Local limits of galton-watson trees conditioned on the number of protected nodes

Résumé

We consider a marking procedure of the vertices of a tree where each vertex is marked independently from the others with a probability that depends only on its out-degree. We prove that a critical Galton-Watson tree conditioned on having a large number of marked vertices converges in distribution to the associated size-biased tree. We then apply this result to give the limit in distribution of a critical Galton-Watson tree conditioned on having a large number of protected nodes.
Fichier principal
Vignette du fichier
protected_revised.pdf (165.46 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01195701 , version 1 (08-09-2015)
hal-01195701 , version 2 (25-04-2016)

Licence

Paternité

Identifiants

Citer

Romain Abraham, Aymen Bouaziz, Jean-François Delmas. Local limits of galton-watson trees conditioned on the number of protected nodes. Journal of Applied Probability, 2017, 54, pp.55-65. ⟨hal-01195701v2⟩
274 Consultations
207 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More