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Title:	Limit theorems for patterns in ranked tree-child networks
Authors:	符麥克 Fuchs, Michael;Liu, Hexuan;Yu, Tsan-Cheng
Contributors:	應數系
Keywords:	limit law;method of moments;pattern;Phylogenetic net-work;ranked tree-child network;tree-child network
Date:	2024-01
Issue Date:	2024-05-24 11:34:18 (UTC+8)
Abstract:	We 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.
Relation:	Random Structures & Algorithms, Vol.64, No.1, pp.15-37
Data Type:	article
DOI 連結:	https://doi.org/10.1002/rsa.21177
DOI:	10.1002/rsa.21177
Appears in Collections:	[應用數學系] 期刊論文

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