# Root estimation in Galton–Watson trees

@article{Brandenberger2022RootEI, title={Root estimation in Galton–Watson trees}, author={Anna Brandenberger and Luc Devroye and Marcel K. Goh}, journal={Random Structures \& Algorithms}, year={2022} }

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.

## 2 Citations

Leaf multiplicity in a Bienaym\'e-Galton-Watson tree

- Mathematics, Computer ScienceDiscrete Mathematics & Theoretical Computer Science
- 2022

This note defines a notion of multiplicity for nodes in a rooted tree and
presents an asymptotic calculation of the maximum multiplicity over all leaves
in a Bienaym\'e-Galton-Watson tree with…

The Horton–Strahler number of conditioned Galton–Watson trees

- Mathematics, Computer Science
- 2020

It is shown that for critical Galton-Watson trees with finite variance conditioned to be of size $n$, the Horton-Strahler number grows as $\frac{1}{2}\log_2 n$ in probability.

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