GLOBAL REGIME FOR GENERAL ADDITIVE FUNCTIONALS OF CONDITIONED BIENAYMÉ-GALTON-WATSON TREES - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Probability Theory and Related Fields Année : 2022

GLOBAL REGIME FOR GENERAL ADDITIVE FUNCTIONALS OF CONDITIONED BIENAYMÉ-GALTON-WATSON TREES

Résumé

We give an invariance principle for very general additive functionals of conditioned Bienaymé-Galton-Watson trees in the global regime when the offspring distribution lies in the domain of attraction of a stable distribution, the limit being an additive functional of a stable Lévy tree. This includes the case when the offspring distribution has finite variance (the Lévy tree being then the Brownian tree). We also describe, using an integral test, a phase transition for toll functions depending on the size and height.
Fichier principal
Vignette du fichier
phase-sept-2020.pdf (761.28 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02941122 , version 1 (16-09-2020)

Identifiants

Citer

Romain Abraham, Jean-François Delmas, Michel Nassif. GLOBAL REGIME FOR GENERAL ADDITIVE FUNCTIONALS OF CONDITIONED BIENAYMÉ-GALTON-WATSON TREES. Probability Theory and Related Fields, 2022, 182 (182), pp.277-351. ⟨10.1007/s00440-021-01095-9⟩. ⟨hal-02941122⟩
98 Consultations
55 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More