English

Conditioning Bienaym{\'e}-Galton-Watson trees to have large sub-populations

Probability 2023-11-30 v1

Abstract

We study the local limit in distribution of Bienaym{\'e}-Galton-Watson trees conditioned on having large sub-populations. Assuming a generic and aperiodic condition on the offspring distribution, we prove the existence of a limit given by a Kesten's tree associated with a certain critical offspring distribution.

Keywords

Cite

@article{arxiv.2311.17716,
  title  = {Conditioning Bienaym{\'e}-Galton-Watson trees to have large sub-populations},
  author = {Romain Abraham and Hongwei Bi and Jean-François Delmas},
  journal= {arXiv preprint arXiv:2311.17716},
  year   = {2023}
}