Consider a population where individuals have two characteristics: a size, which is a positive integer, and a type, which is a member of a finite set. This population reproduces in a Galton-Watson fashion, with one additional condition: given that an individual has size $n$, the sum of the sizes of its children is less than or equal to n. We call multi-type Markov branching tree the family tree of such a population.

We show that under some assumptions about the splitting rates, Markov branching trees have scaling limits in distribution which are self-similar fragmentation trees, monotype or multi-type.

We then give two applications: the scaling limits of some growth models of random trees, and new results on the scaling limits of multi-type Galton-Watson trees.

This is joint work with Bénédicte Haas.

**Date**: 16 February 2022, 12:00 (Wednesday, 5th week, Hilary 2022)**Venue**: Mathematical Institute

Woodstock Road OX2 6GGSee location on maps.ox**Details**: Room L3**Speaker**: Robin Stephenson (University of Sheffield)**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)**Part of**: Probability seminar**Booking required?**: Not required**Audience**: Public- Editors: Christina Goldschmidt, James Martin, Matthias Winkel