A Study of the Random Recursive Tree

Link to Join MS Teams Talk

This talk will be broadcast at 15:00 BST 26th April on MS Teams only.

Meeting ID: 393 527 089 878
Passcode: dsm7py

Abstract

The random recursive tree is a random labelled tree of size n, sampled uniformly from all increasing trees of size n (trees with increasing labels on paths away from the root). It is a classical model of randomly grown trees that has been thoroughly studied ever since its introduction in the 1980’s and holds connections with many other discrete random objects. We will investigate the joint behaviour of the degree, depth, and label of, and graph distance between high-degree vertices in the random recursive tree. The analysis of the label of and graph distance between high-degree vertices is novel, in particular in relation to the behaviour of the depth of such vertices (whose known results we also improve and extend). The analysis is based on a correspondence between the random recursive tree and a representation of Kingman’s n-coalescent.

About Bas

Bas Lodewijks is a postdoc within the probability group of the Institut Camille Jordan at the University of Lyon and the University of Saint-Etienne, working with Dieter Mitsche. Previously, he completed his PhD within the probability group (Prob-L@b) of the University of Bath, supervised by Marcel Ortgiese.

His main interests are in random graph theory, particularly evolutionary and/or spatial random graph models. Such models are not only interesting from a mathematical perspective, but also provide insights in networks in many real-world applications.

He graduated the University of Technology in Eindhoven, the Netherlands, in 2018 after completing a Bachelor and Master of Science in Industrial and Applied Mathematics there. His master thesis was supervised by Julia Komjathy.