Research Group Probability Theory

Probability theory: recognizing structure within randomness

Probability theory is applied in many areas such as biology, computer science, actuarial sciences
and physics. In addition, it has many connections to other areas of mathematics, such as analysis, graph theory and mathematical physics.

Our group is active in the following areas of probability theory: 

• with stochastic processes such as random walks in random networks and environments as models for transport in inhomogeneous medium.
• with random walks with self-interaction, for example, self-reinforcing and self-repelling random walks. These models offer fascinating mathematical challenges and contribute to the understanding of self-reinforcing effects within complex biological systems.
• with the research of randomized processes in signal processing and data analysis. These can often be described with the assistance of structured random matrices and then analyzed using methods from probability theory.
• with interacting particle systems. These can e.g. describe physical systems.
• with the research of random growth processes, which model a variety of real world growth processes such as dielectric breakdowns, growth of colonies of bacteria under lack of nutritions, growth of dendrites in batteries and a variety of other processes.