Previous projects

Research training school (RTG) 2131

High-dimensional Phenomena in Probability -
Fluctuations and Discontinuity

The Research Training Group (RTG) High-dimensional Phenomena in Probability - Fluctuations and Discontinuity offers excellent national and international graduates in the mathematical sciences the opportunity to conduct internationally visible doctoral research in probability theory. The goal of the RTG is to bring together the joint expertise on aspects of high dimension in probability. In the study of random structures in high dimensions, one frequently observes universality in limit theorems (fluctuations) as well as phase transitions (discontinuities). These aspects form the common focus of a large number of currently active research projects in stochastic processes. The cooperation of several research groups will offer the Ph.D. students the unique opportunity to gain experience beyond their own research topic, thus giving a broad scientific education. The RTG is supported by top level research groups in probability theory and its applications, stochastic analysis, stochastic geometry and mathematical physics. The research groups involved in the RTG have recently successfully carried out externally funded research projects in probability and statistics. As a rule, each doctoral student in the RTG will be supervised by two PIs.

Further information

Priority Program (SPP 1590)

Probabilistic Structures in Evolution

Project: Evolving pathogen phylogenies: a two-level branching approach - Anita Winter

For many RNA viruses the lack of a proofreading mechanism in the virus' RNA polymerase results in frequent mutation. The high viral mutation rates, the large virus population size, and the short replication periods produce abundance of viral variability which is responsible for immune escape or drug resistance. Understanding in detail the forces which maintain this diversity can assist in the struggle against viral infections.
Pathogen patterns - and in particular the shapes of the phylogenies - are affected by the strength of selective pressure due to various levels of cross-immunity. We focus on the temporal structure of phylogenies associated with a persistent virus. We propose a two-level (host-pathogen) branching model with mutation and competition on both levels in dierent scaling regimes, where hosts can be either the infected patients or the infected cells within a single patient. We thereby extend our recent work on a panmitic virus population.
We will further rely on techniques developed for measure-valued (neutral) multilevel branching dynamics and two-level multi-type branching dynamics with mutation and competition.


Further information


SFB/ Transregio (TRR 12 - A 7)

Symmetries and Universality in Mesoscopic Systems



Fluctuations and large deviations in nonequilibrium stochastic dynamics
A. Altland, TP Köln, E. Frey, ASC München, J. Krug, TP Köln, C. Külske, M Bochum, A. Winter, M Duisburg-Essen
The project explores fluctuation-dominated behavior in interacting many-body systems originating from a variety of physical and biological contexts. A common methodological basis is provided by the use of large deviations principles in path space, which links the project to dynamical systems theory and semi-classical quantum mechanics. Specific problems to be addressed concern the structure of none-equilibrium measures in spin systems, fluctuation theorems for mesoscopic quantum systems, and effects of demographic and spatial fluctuations in models of biological population dynamics.