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A branching process approach to level‐ k phylogenetic networks
Author(s) -
Stufler Benedikt
Publication year - 2022
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.21065
Subject(s) - branching process , mathematics , branching (polymer chemistry) , context (archaeology) , excursion , random graph , phylogenetic tree , process (computing) , tree (set theory) , convergence (economics) , brownian excursion , stochastic process , random tree , combinatorics , discrete mathematics , computer science , artificial intelligence , statistics , diffusion process , geography , geometric brownian motion , graph , materials science , law , economic growth , knowledge management , innovation diffusion , robot , composite material , operating system , biochemistry , political science , motion planning , economics , gene , chemistry , archaeology
The mathematical analysis of random phylogenetic networks via analytic and algorithmic methods has received increasing attention in the past years. In the present work we introduce branching process methods to their study. This approach appears to be new in this context. Our main results focus on random level‐ k networks with n labeled leaves. Although the number of reticulation vertices in such networks is typically linear in n , we prove that their asymptotic global and local shape is tree‐like in a well‐defined sense. We show that the depth process of vertices in a large network converges towards a Brownian excursion after rescaling byn − 1 / 2. We also establish Benjamini–Schramm convergence of large random level‐ k networks towards a novel random infinite network.