Aim:

Funding period 2006/08:

This research group will create an intense interaction between analysis and probability theory to investigate physical systems with random input and high degree of complexity. It will bring together and further develop ideas and methodologies from both areas to derive results that are out of reach for each of the disciplines alone. The range of our subjects comprises interface models with gradient interactions, the Cauchy-Born rule at positive temperatures, intermittency in random media, phase boundaries with random perturbations, and interacting Brownian motions and functional integration for many-body systems at low temperatures. The methods we will apply consist of an appropriate combination of tools from analysis (e.g., variational calculus, weak convergence methods, spectral theory, and homogenization) and probability theory (e.g., large deviations, stochastic analysis, ergodic theory, and Gibbs measures).

Funding period 2009/11:

In the extension of our research group, our goal continues to be the systematic combination of methods from analysis (e.g., variational calculus, weak convergence methods, spectral theory, and homogenisation) and probability theory (e.g., large deviations, stochastic analysis, ergodic theory, and Gibbs measures) to analyse large physical systems with complex interactions and random input. We continue to study mostly the same models as so far, such as interface models with gradient interactions, the Cauchy-Born rule at positive temperatures, random media, phase boundaries with random perturbations, and interacting Brownian motions and functional integration for many-body systems. Now we will build on our achievements in the first funding period and will study deeper problems that are now within reach thanks to our recent work, like fluctuations in non-convex perturbation of massless Hamiltonians, aging and hopping dynamics, Bose-Einstein condensation, moving material singularities.