The group contributes to the following mathematical research topics of WIAS:

Interacting stochastic particle systems

In the mathematical modeling of many processes and phenomena in the Sciences and Technology one employs systems with many random particles and interactions. In this context, we define the term "particle systems" very broadly and also include point processes with percolation properties and random graph structures as well as Gibbs interactions. It also includes random movements of these particles, such as those that occur in spatial models for communication. At WIAS, many macroscopic properties of these particle systems are investigated that arise from the microscopic rules, such as phase transitions (condensation, percolation, crystallization) and critical properties such as rescaling limits. [>> more]

Large deviations

The theory of large deviations, a branch of probability theory, provides tools for the description of the asymptotic decay rate of a small probability, as a certain parameter diverges or shrinks to zero. Examples are large times, low temperatures, large numbers of stochastic quantities, or an approximation parameter. This probabilistic theory is also indispensable in the treatment of a number of models in statistical physics, as it makes them accessible for analysis using variational techniques. Both theory and sophisticated applications in physics and chemistry are being investigated at WIAS. [>> more]

Random geometric systems

Systems with many random components distributed in space (points, edges, graphs, trajectories, etc.) with many short- or long-range interactions are examined at the WIAS for their macroscopic properties. Particular attention is paid to the formation of particularly large structures in the system or other phase transitions. [>> more]