Areas of research

Below you can find a selection of topics that are of interest to the group.

Random Networks

Many of the phenomena in the complex world in which we live have a rough description as a large network of interacting components. Random network theory tries to describe the global structure of such networks from basic local principles using stochastic models. Models we are interested in include preferential attachment networks, spatially embedded networks and time-dependent inhomogeneous random graphs.

Selected papers on this topic:
Interacting Particle Systems

It is a crucial challenge in probability to understand the emergent behaviour of systems of particles interacting with each other or with an external environment when the system size is increasing. Research in our group is using large deviation theory as well as multiscale analysis to understand the limiting behaviour of a range of models, including infections spreading on particles migrating in space.

Selected papers on this topic:
Stochastic Processes in Random Environments

We are interested in the problem how an inhomogeneous environment can influence the behaviour of a stochastic process taking place in such an environment. Examples studied in our group include diffusion process in an irregular random potential (parabolic Anderson model) and infection processes on inhomogeneous random networks. The general phenomena observed in this context include ageing, intermittency and metastability.

Selected papers on this topic:
Condensation Phenomena

Condensation occurs in a system if a proportion of a distributed observable quantity concentrates asymptotically in a single location. The physical phenomenon of Bose-Einstein condensation (where the observed quantity is energy and a positive fraction of bosons occupy the lowest quantum state) is just one example. We are interested in the dynamics of the condensation process for a range of models exhibiting condensation, including stochastic processes with reinforcement, the zero-range process, and non-stochastic (PDE based) models.

Selected papers on this topic: