Root estimation in Galton-Watson trees
arXiv:2007.05681
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.
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