Probability Seminar: Gabriel Berzunza Ojeda - Fringe trees for random trees with given vertex degrees.
| Dates: | 8 October 2025 |
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| Times: | 15:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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Gabriel Berzunza Ojeda (University of Liverpool) will speak at the Probability seminar.
Title: Fringe trees for random trees with given vertex degrees
Abstract: In this talk, we consider fringe trees of random plane trees with given vertex statistics (i.e., a given number of vertices of each degree). The main results are laws of large numbers and central limit theorems for the number of fringe trees of a given type.
The key tool for our proofs is an extension to the multivariate setting of a theorem by Gao and Wormald (2004), which provides a way to show asymptotic normality by analyzing the behaviour of sufficiently high factorial moments.
Our results also apply to random simply generated trees (or conditioned Galton–Watson trees) by conditioning on their degree statistic.
Joint work with Cecilia Holmgren and Svante Janson (Uppsala University)
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Frank Adams 2
Alan Turing Building
Manchester
