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arXiv · 2105.14227

The expected degree distribution in transient duplication divergence models

A. D. Barbour·Tiffany Y. Y. Lo
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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.

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A. D. Barbour, Tiffany Y. Y. Lo. 2021-05-29. The expected degree distribution in transient duplication divergence models. https://arxiv.org/abs/2105.14227

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