Statistical Analysis and Stochastic Modelling of Complex Systems
Head of group: Eule, StephanThe dynamics of many systems in nature is too complicated to be described ab initio. Today, the investigation of such complex systems plays an important role, not only in physics, but in many fields of science. In general, such systems are in a state far from equilibrium, i. e. they are exposed to a constant flux of energy. Therefore, a common feature of complex systems is the occurrence of intricate fluctuations which can be induced either by a complex environment or stem from internal dynamics. To describe these systems, one applies the mathematical theory of stochastic processes. The research interests of our group range from the application of stochastic processes to biological, ecological and socioeconomic systems to the mathematical generalization of stochastic processes to account for systems which exhibit anomalous diffusion. Thereby an interdisciplinary approach is employed, applying methods from statistical mechanics, network theory and game theory.
Projects:

Statistical Properties of Order BooksIn recent years there have been considerable efforts to employ methods from theoretical physics to problems in economics. Our group is interested in the dynamics of the order book, which can be seen as the ultimate microscopic level of description of financial markets.


Dynamics and Control of Infectious DiseasesThe sudden appearance and rapid spread of an infectious diseases can pose a serious threat to human or animal populations that calls for immediate actions by national and international health agencies. Their response is guided by epidemiological models whose primary use is to provide means of comparing the effectiveness of different containment strategies. The focus
of our group is to quantify, how heterogeneity of the infection process affects the course of an infectious disease. In particular, we are interested in the effect of indiviudal variation in disease transmission on control strategies in the early phase of an epidemic outbreak and
the consequences of spatially varying infection rates on travel restrictions.


Anomalous Stochastic ProcessesIf the timeevolution of the meansquared displacement of some quantity is nonlinear,
the system is said to exhibit anomalous diffusion. The underlying mechanisms leading to such anomalous diffusion can be multifold. Our group focuses on processes whose
anomalous behavior is due to heavytailed distributions of either the waiting time
distribution between the displacements or of the displacements themselves.

People working in this Group:
Name  Phone  

Stephan Eule  send email  [+49(0)5515176411] 
Theo Geisel  send email  [+49(0)5515176400] 
Nicolas Lenner  send email  [+49(0)5515176421] 