Project Details
Projekt
FOR 718: Analysis and Stochastics in Complex Physical Systems
Subject Area
Mathematics
Term
from 2006 to 2014
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 20967890
This Research Unit 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 homogenisation) and probability theory (e.g., large deviations, stochastic analysis, ergodic theory and Gibbs measures).
Analysis and Stochastics have been developing rapidly, but separately, for decades. Although certain cross-connections already exist, there is strong belief that a high-level cooperation between the two fields is needed for significant further progress. In particular, in the fields of statistical mechanics, interacting particle systems and materials science, it has become clear that the success of the research crucially depends on an equally highly developed expertise in analysis and probability theory. We are aware of the fact that there is a certain language barrier between the two fields of analysis and stochastics. This may be the reason why there are only very few places in the world where a systematic and organised cooperation between these two fields for the investigation of complex physical systems has been instituted yet.
One of our goals is to surmount this barrier. Another goal is the integration of high-class junior researchers into the research on our subjects, by making young postdocs with probabilistic expertise acquainted with problems and methods from analysis and mathematical physics, and by involving analytically trained postdocs into stochastically motivated projects and probabilistic methods. In our Berlin-Leipzig seminar, regular talks on all the involved subjects, given by group members and guests, present the latest and relevant research directions.
Analysis and Stochastics have been developing rapidly, but separately, for decades. Although certain cross-connections already exist, there is strong belief that a high-level cooperation between the two fields is needed for significant further progress. In particular, in the fields of statistical mechanics, interacting particle systems and materials science, it has become clear that the success of the research crucially depends on an equally highly developed expertise in analysis and probability theory. We are aware of the fact that there is a certain language barrier between the two fields of analysis and stochastics. This may be the reason why there are only very few places in the world where a systematic and organised cooperation between these two fields for the investigation of complex physical systems has been instituted yet.
One of our goals is to surmount this barrier. Another goal is the integration of high-class junior researchers into the research on our subjects, by making young postdocs with probabilistic expertise acquainted with problems and methods from analysis and mathematical physics, and by involving analytically trained postdocs into stochastically motivated projects and probabilistic methods. In our Berlin-Leipzig seminar, regular talks on all the involved subjects, given by group members and guests, present the latest and relevant research directions.
DFG Programme
Research Units
Projects
- Dynamic large deviations: nucleation and growth in phase transitions and avalanches in random hamiltonian systems (Applicant Röger, Matthias )
- Effective interface models with gradient interactions and the Cauchy-Born rule at positive temperature (Applicants Deuschel, Jean-Dominique ; Luckhaus, Stephan )
- Intermittency phenomena in random media (Applicant Gärtner, Jürgen )
- Kooperationsfond (Applicant König, Wolfgang )
- Many-body systems, interacting brownian motions, and functional integrals (Applicant König, Wolfgang )
- Multi-scale analysis of phase boundaries under the influence of fluctuations and random fields (Applicant von Renesse, Max-Konstantin )
- Systems with many degrees of freedom: probalistic and constructive field theory methods (Applicants König, Wolfgang ; Salmhofer, Manfred )
Spokesperson
Professor Dr. Wolfgang König
