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. 
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