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We give an invariance principle for very general additive functionals of conditioned Bienayme-Galton-Watson trees in the global regime when the offspring distribution lies in the domain of attraction of a… Click to show full abstract
We give an invariance principle for very general additive functionals of conditioned Bienayme-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 Levy tree. This includes the case when the offspring distribution has finite variance (the Levy 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.
Journal Title: Probability Theory and Related Fields
Year Published: 2021
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