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Global Regime for General Additive Functionals of Conditioned Bienaym{\'e}-Galton-Watson Trees
- Publication Year :
- 2020
-
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.
- Subjects :
- Mathematics - Probability
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2009.08185
- Document Type :
- Working Paper