GLOBAL REGIME FOR GENERAL ADDITIVE FUNCTIONALS OF CONDITIONED BIENAYMÉ-GALTON-WATSON TREES
| Autor: | Romain Abraham, Jean-François Delmas, Michel Nassif |
|---|---|
| Přispěvatelé: | Institut Denis Poisson (IDP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO), Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique (CERMICS), Institut National de Recherche en Informatique et en Automatique (Inria)-École des Ponts ParisTech (ENPC), Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), École des Ponts ParisTech (ENPC), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
010102 general mathematics 01 natural sciences Galton-Watson trees [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] 010104 statistics & probability Mathematics::Probability phase transition scaling limit 0101 mathematics Statistics Probability and Uncertainty additive functionals Analysis Mathematics - Probability Lévy trees |
| Zdroj: | Probability Theory and Related Fields Probability Theory and Related Fields, 2022, 182, pp.277-351 |
| ISSN: | 0178-8051 1432-2064 |
| Popis: | International audience; 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. |
| Databáze: | OpenAIRE |
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