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Scaling limits of multi-type Markov Branching Trees
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
Venue:
Mathematical Institute, Woodstock Road OX2 6GG
Venue 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
