Root estimation in Galton-Watson trees

TL;DR

This paper investigates the problem of estimating the root node in a size-conditioned Galton-Watson tree based solely on its free-tree structure, providing a maximum-likelihood estimator and analyzing its accuracy.

Contribution

It introduces the maximum-likelihood estimator for root identification in Galton-Watson trees and computes its success probability, advancing understanding of root inference in random trees.

Findings

Maximum-likelihood estimator for root identification

Probability of correct root estimation calculated

Theoretical analysis of estimator's performance

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.