Many interesting applications from physics or biology, such as the understanding of transport processes in porous media or the evolution of populations, can be efficiently modelled through stochastic processes in a random medium. Characteristic of random media is the occurrence of strong spatial or temporal inhomogeneities on microscopic scales. In contrast, on macroscopic scales, that is, on length or time scales that are significantly larger compared to the microscopic inhomogeneities, a homogenisation effect can typically be observed. This allows the dynamic behaviour of the system to be described by an effective stochastic process in a homogeneous, deterministic medium. It is of mathematical interest to understand under what conditions homogenisation occurs in the random medium and what the relationship is between the microscopic inhomogeneities on one hand and the effective homogeneous quantities on the macroscopic level on the other.

• metastable behaviour of Markov processes
• functional inequalities related to the longtime behaviour of stochastic processes
• scaling limits of stochastic processes in random media
• population genetics