English

Constructing and searching conditioned Galton-Watson trees

Probability 2014-12-19 v1

Abstract

We investigate conditioning Galton-Watson trees on general recursive-type events, such as the event that the tree survives until a specific level. It turns out that the conditioned tree is again a type of Galton-Watson tree, with different types of offspring and a level-dependent offspring distribution, which will all be given explicitly. As an interesting application of these results, we will calculate the expected cost of searching a tree until reaching a given level.

Keywords

Cite

@article{arxiv.1412.5890,
  title  = {Constructing and searching conditioned Galton-Watson trees},
  author = {Eric Cator and Henk Don},
  journal= {arXiv preprint arXiv:1412.5890},
  year   = {2014}
}

Comments

16 pages, 2 figures

R2 v1 2026-06-22T07:36:57.223Z