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We study the degree distribution of a randomly chosen vertex in a duplication–divergence graph, paying 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. This is joint work with A. D. Barbour.
