English

Root estimation in Galton-Watson trees

Probability 2024-07-08 v3

Abstract

Given only the free-tree structure of a tree, the root estimation problem asks if one can guess which of the free tree's nodes is the root of the original tree. We determine the maximum-likelihood estimator for the root of a free tree when the underlying tree is a size-conditioned Galton-Watson tree and calculate its probability of being correct.

Keywords

Cite

@article{arxiv.2007.05681,
  title  = {Root estimation in Galton-Watson trees},
  author = {Anna M. Brandenberger and Luc Devroye and Marcel K. Goh},
  journal= {arXiv preprint arXiv:2007.05681},
  year   = {2024}
}

Comments

24 pages, TeX; the main change is that Section 3 has been removed and its proofs incorporated into other sections; various other small fixes and changes for readability

R2 v1 2026-06-23T17:02:15.501Z