Romain Abraham, Jean-François Delmas, Michel Nassif
Published 2020-09-17Version 1
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.
On the invariance principle for empirical processes of associated sequences
Conditioning (sub)critical L{é}vy trees by their maximal degree: Decomposition and local limit
Invariance principle for Lifts of Geodesic Random Walks
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