The expected degree distribution in transient duplication divergence models
Probability
2021-06-01 v1 Molecular Networks
Abstract
We study the degree distribution of a randomly chosen vertex in a duplication--divergence graph, under a variety of different generalizations of the basic model of Bhan, Galas and Dewey (2002) and V\'azquez, Flammini, Maritan and Vespignani (2003). We pay particular attention to what happens when a non-trivial proportion of the vertices have large degrees, establishing a central limit theorem for the logarithm of the degree distribution. Our approach, as in Jordan (2018) and Hermann and Pfaffelhuber (2021), relies heavily on the analysis of related birth--catastrophe processes, and couplings are used to show that a number of different formulations of the process have asymptotically similar expected degree distributions.
Cite
@article{arxiv.2105.14227,
title = {The expected degree distribution in transient duplication divergence models},
author = {A. D. Barbour and Tiffany Y. Y. Lo},
journal= {arXiv preprint arXiv:2105.14227},
year = {2021}
}