This proposal is for a major international research and education collaboration in several overlapping areas of Probability Theory, Statistical Physics, Complex Analysis and Geometry such as Schramm-Loewner Evolutions, Critical and near-critical Percolation, Random Networks, Self-Interacting Random Walks, and, more generally, geometric/stochastic aspects of Disordered Systems.
The project concerns various aspects of random spatial processes, called “percolative systems”, in which macroscopic phenomena are naturally expressed in terms of paths of microscopic events that percolate through space (or space-time). Scaling concepts and renormalization methods play an important role in the analysis of such processes, the nature of their phase transitions and critical behavior. Themes that will be studied are:
- Scaling limits of two-dimensional percolation-type models and the Schramm-Loewner Evolution;
- Random planar maps;
- Quantum Gravity, Conformal Loop Ensembles (CLE) and the Gaussian Free Field;
- Large scale phenomena and Universality in Random Networks;
- RWREs, Self-Interacting Walks, Statistical Physics in Random Environment;
- Rigorous Renormalization and Super-Symmetry methods in disordered systems;
- Coarse Geometry of Random Systems;
- Anomalous fluctuations in non-equilibrium systems.
These and related problems are challenging, but are ripe for a collaborative attack combining the diverse expertise of the participants from Europe and abroad. One of the main goals of this proposal is to exhibit and clarify the close relationship between these questions.
The collaborators of proposed network have been prime participants in some of the major progress in this field. The proposed Network will have partnerships with other European and Non-European Networks and Programs (PIRE-NSF), Prosul (CNPq-Brazil)).
Training and extensive mentoring will be provided to postdoctoral, graduate and advanced undergraduate students from various backgrounds.
This proposal aims to create a self-sustaining model of enhanced collaboration at faculty, postdoctoral and student levels not only between the European research institutions, but also between European, U.S. and Latin American universities.
Scaling Limits; Schramm-Loewner Evolution; Gaussian Free Field, Conformal Loop Ensembles; Random planar maps, Random networks in random environment, Self-interacting Random Walks, Renormalization Group, Super-Symmetry Methods, Non-equilibrium phase transitions and fluctuations.