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
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