I studied for a Maths degree at the University of Nottingham, and then I completed a masters degree in Computational Science at Imperial College London. I am generally interested in computational maths, optimisation and numerical analysis. I have also recently developed an interest in probability and statistics.

Project title:
Voronoi cells in split trees with heavy-tailed split distribution

Supervisor(s):
Cecile Mailler

Project description:
A Voronoi tessellation on a graph G is a partition of G into k Voronoi cells, with the nucleus of each cell being a node of the graph. The cells are constructed so that any node inside one cell is closer to the nucleus of its cell than to any other nucleus, with respect to the graph distance. Existing work has shown that the limiting vector for this partition on the uniform tree follows a uniform distribution on the k-dimensional simplex. In contrast, results for random split trees with a light-tailed split distribution exhibit a winner takes all behaviour. The goal of this project is to study the sizes of Voronoi cells on random split trees with a heavy-tailed split distribution.