Tom graduated from Bath in 2017 with an MMath and is particularly interested in analysis and probability. He completed a summer project on the mixing times of load balancing schemes and his final year project used the close relationship between random walks, martingales, and harmonic functions to explicitly find the potential kernel for the simple random walk on the hexagonal lattice. Apart from Maths, Tom’s favourite things include cricket, handball, obscure Simpsons’ references, and films by Paul Thomas Anderson.

Research project title:
Multi-particle diffusion limited aggregation

Supervisor(s):
Alexandre Stauffer

Project description:
Multi-particle diffusion limited aggregation (MDLA) was formulated as a tractable model for dendritic growth. Unfortunately, geometric and dynamic properties of it have evaded a strong mathematical treatment for decades and understanding the behaviour of MDLA remains an open challenge. For example, under certain parameters MDLA may observe some limiting shape at macroscopic scales, but at the mesoscopic and microscopic scales will have complex and fractal-like structure. A competition model called ’first passage percolation in a hostile environment’ (FPPHE) has been successfully coupled with MDLA to show a phase of linear growth exists. Tom’s project investigates these links further and attempts to prove stronger results for FPPHE, such as the existence of a ’co-existence’ phase between the competing growth processes. The project also aims to understand variants of MDLA better, such as 24a Poissonized version of MDLA, whereby there is initially a Poisson cloud of particles, and each particle performs a random walk until aggregated. In one dimension the critical value for the initial density is 1 for linear growth, but in higher dimensions it is conjectured to be 0, and this project aims to prove this and related results.