PC Seminar: Fringe trees for random trees with given vertex degrees
- Date: 13 April 2023, 11:15–12:15
- Location: Ångström Laboratory, Å64119
- Type: Seminar
- Lecturer: Gabriel Berzunza Ojeda (University of Liverpool)
- Organiser: Matematiska institutionen
- Contact person: Tiffany Lo
Welcome to this seminar held by Gabriel Berzunza Ojeda (University of Liverpool) with the 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, and to random labelled trees with given vertex degrees.
Joint work with Cecilia Holmgren and Svante Janson (Uppsala University).
This is a seminar in our seminar series on Probability and Combinatorics (PC).