Branching processes

Project ID: 2228cd1431 (You will need this ID for your application)

UCL Lead department: Statistical Science

Project Summary:

Branching processes are a topic in probability theory, offering a model of a collection of “cells” which change and divide. Each cell has some associated trait, such as mass. As time passes, the trait changes (e.g., the cell grows) and eventually the cell divides into two new cells, which have the same behaviour.

Models like this are widely used in biology and physics, but they also have significant theoretical interest, which is the focus of this project. One interesting property is that as time progresses, the cell trait distribution typically settles down into a steady state, which can be described. Another is that as the initial number of cells is made large, the random evolution of the model reduces to a deterministic one, possibly with a random component. The project is to investigate these “asymptotic” (large time or large cell count) properties. When do they hold, and when not? How can we describe the “limit” objects? And how does the presence of interactions, such as direct or indirect competition, change the situation?

As this project concerns probability theory, you should have a solid mathematical background with a good understanding of stochastic processes (particularly Markov processes), measure theory and martingales.