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Global Regime for General Additive Functionals of Conditioned Bienaym{é}-Galton-Watson Trees

We give an invariance principle for very general additive functionals of conditioned Bienaym{é}-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{é}vy tree. This includes the case when the offspring distribution has finite variance (the L{é}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.

preprint2020arXivOpen access
Romain AbrahamJean-François DelmasMichel Nassif
math.PR
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Open access3 authors1 topic
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Romain AbrahamJean-François DelmasMichel Nassif

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