More about the programme
In equilibrium, the main concern is the rigorous treatment of spin systems, polymers, interfaces, and disordered media. This needs a mathematical understanding of the interplay between different space-time scales through renormalisation-group methods in combination with multi-scale perturbation techniques.
Out of equilibrium, the main emphasis is on metastability, hydrodynamic behaviour of conservative systems, the microscopic elucidation of entropy production, and properties of granular media.
Points of departure are model systems subject to a random dynamics. The microscopic dynamics defines a transformation on the phase space of the system, which typically is very complex. The important challenge is to give a precise mathematical treatment of the interesting physics that arises from this complexity. The concept of entropy is essential in connecting the microscopic dynamics with the macroscopic phenomena. Mathematically, fluctuation theory and large deviation theory provide this connection. The macroscopic behaviour arises from an appropriate space-time rescaling in combination with probabilistic limit theorems.
The main goal of the collaboration is to bring together the core of the researchers in Europe that are active in this subarea of mathematical statistical physics.
Keywords: Spatially extended systems, random dynamics, fluctuation theory, large deviation theory, long-range dependence, anomalous fluctuation phenomena, phase transitions
Status of the research context, of the goals and of the envisaged achievements of the programme initiative:
The programme centres around the following research topics:
- (a) Gibbsian vs. non-Gibbsian spin systems.
- (b) Polymers and self-interacting random processes.
- (c) Interfaces and surface phenomena.
- (d) Disordered media.
- (e) Relaxation to equilibrium and metastability.
- (f) Hydrodynamic behaviour of conservative systems.
- (g) Entropy production and fluctuations far from equilibrium.
- (h) Granular media and sandpile dynamics.
