GLOBAL REGIME FOR GENERAL ADDITIVE FUNCTIONALS OF CONDITIONED BIENAYMÉ-GALTON-WATSON TREES - Archive ouverte HAL Access content directly
Journal Articles Probability Theory and Related Fields Year : 2022

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

Abstract

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.
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Dates and versions

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

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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⟩
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