Distribution of tree parameters by martingale approach
Combinatorics
2022-06-16 v2
Abstract
For a uniform random labelled tree, we find the limiting distribution of tree parameters which are stable (in some sense) with respect to local perturbations of the tree structure. The proof is based on the martingale central limit theorem and the Aldous--Broder algorithm. In particular, our general result implies the asymptotic normality of the number of occurrences of any given small pattern and the asymptotic log-normality of the number of automorphisms.
Keywords
Cite
@article{arxiv.1912.09838,
title = {Distribution of tree parameters by martingale approach},
author = {Mikhail Isaev and Angus Southwell and Maksim Zhukovskii},
journal= {arXiv preprint arXiv:1912.09838},
year = {2022}
}