Title
Distribution of tree parameters by martingale approach.
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.
Year
DOI
Venue
2022
10.1017/S0963548321000523
Combinatorics, Probability & Computing
DocType
Volume
Issue
Journal
31
5
ISSN
Citations 
PageRank 
0963-5483
0
0.34
References 
Authors
0
3
Name
Order
Citations
PageRank
Isaev Mikhail100.34
Southwell Angus200.34
Maksim Zhukovskii324.51