Scaling limits of Markov Branching Trees

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• Robin Stephenson, University of Oxford
• Thursday 04 October 2018, 15:00-16:00
• Watson LTB.

If you have a question about this talk, please contact Henning Sulzbach.

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.

As a generalisation of the results of Haas and Miermont on monotype Markov branching trees, we show that under some assumptions (mainly that macroscopic dislocation of a large fragment are rare), Markov branching trees have scaling limits in distributions 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.

This talk is part of the Combinatorics and Probability seminar series.

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• Combinatorics and Probability seminar
• School of Mathematics events
• Watson LTB

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