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.

**Date**: 6 February 2023, 14:00 (Monday, 4th week, Hilary 2023)**Venue**: Mathematical Institute

Woodstock Road OX2 6GGSee location on maps.ox**Details**: L3**Speaker**: Tiffany Lo (Uppsala University)**Organising department**: Department of Statistics**Organisers**: Matthias Winkel (Department of Statistics, University of Oxford), Christina Goldschmidt (Department of Statistics, University of Oxford), James Martin (Department of Statistics, University of Oxford), Julien Berestycki (University of Oxford)**Part of**: Probability seminar**Booking required?**: Not required**Audience**: Public- Editor: Christina Goldschmidt