Global Regime for General Additive Functionals of Conditioned Bienaym{\'e}-Galton-Watson Trees
Probability
2020-09-18 v1
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.
Keywords
Cite
@article{arxiv.2009.08185,
title = {Global Regime for General Additive Functionals of Conditioned Bienaym{\'e}-Galton-Watson Trees},
author = {Romain Abraham and Jean-François Delmas and Michel Nassif},
journal= {arXiv preprint arXiv:2009.08185},
year = {2020}
}