Affiliation:
1. Department of Mathematical Sciences National Chengchi University Taipei Taiwan
Abstract
AbstractWe prove limit laws for the number of occurrences of a pattern on the fringe of a ranked tree‐child network which is picked uniformly at random. Our results extend the limit law for cherries proved by Bienvenu et al. (Random Struct. Algoritm. 60 (2022), no. 4, 653–689). For patterns of height 1 and 2, we show that they either occur frequently (mean is asymptotically linear and limit law is normal) or sporadically (mean is asymptotically constant and limit law is Poisson) or not all (mean tends to 0 and limit law is degenerate). We expect that these are the only possible limit laws for any fringe pattern.
Subject
Applied Mathematics,Computer Graphics and Computer-Aided Design,General Mathematics,Software
Reference22 articles.
1. Combinatorial and stochastic properties of ranked tree‐child networks
2. Wiley Series in Probability and Mathematical Statistics, A Wiley‐Interscience Publication;Billingsley P.,1995
3. Counting and enumerating tree-child networks and their subclasses
4. Limit theorems for patterns in phylogenetic trees
5. Y.‐S.Chang M.Fuchs H.Liu M.Wallner andG.‐R.Yu.Enumeration ofd$$ d $$‐combining tree‐child networks. LIPICS Proceedings of the 33rd International Meeting on Probabilistic Combinatorial and Asymptotic Methods for the Analysis of Algorithms 225 Paper 5 (2022).
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献