Preferential attachment networks with fitness

This PhD project is based in a modern area of probability at the intersection of random graphs, branching processes and processes in random environments.

The main topic of the project is the analysis of growing network models. Following the paradigm of preferential attachment, these models offer a simple explanation to why power laws can be observed in real-life networks such as the world wide web. The basic rule is that when new nodes are introduced into the network, they prefer to establish connections to old nodes that already have many connections. There are many variations of these processes that have been studied over the last years.

In this project we will consider the preferential network model with fitness. Here, the classical preferential attachment mechanism is modified by equipping each node with a random fitness. This models the fact that not every new node in a real-life network has the same initial attractiveness. The aim of the project is to understand how this extra randomness modifies the structure of the network. The mathematical analysis is closely related to studying processes in random environment and in particular to non-homogeneous branching processes.

The project will be based at the internationally recognised probability laboratory at the University of Bath and the PhD candidate would benefit from a vibrant research environment and the interaction with other postgraduate students and other specialists working on closely related topics.

Anticipated start date: 2 October 2017.

Applicants should apply online for a PhD in Statistics quoting the project title and lead supervisor name on the application form. More information on how to apply may be found here: http://www.bath.ac.uk/science/graduate-school/research-programmes/how-to-apply/

Applications may close early if a suitable candidate is found; therefore, early application is recommended.