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arXiv · 2009.08185

Global Regime for General Additive Functionals of Conditioned Bienaym{\'e}-Galton-Watson Trees

Romain Abraham·Jean-François Delmas·Michel Nassif
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Abstract

We give an invariance principle for very general additive functionals of conditioned Bienaym{\'e}-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 L{\'e}vy tree. This includes the case when the offspring distribution has finite variance (the L{\'e}vy 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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Romain Abraham, Jean-François Delmas, Michel Nassif. 2020-09-17. Global Regime for General Additive Functionals of Conditioned Bienaym{\'e}-Galton-Watson Trees. https://arxiv.org/abs/2009.08185

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