Random Geometric Systems
Welcome to the homepage of the new DFG Priority Programme "Random Geometric Systems" (SPP 2265 "Zufällige geometrische Systeme").
This Priority Programme is coordinated by
with the programme committee:
- Wolfgang König (Technische Universität Berlin and Weierstraß-Institut Berlin)
- Nina Gantert (Technische Universität München (TUM))
- Günter Last (Karlsruhe Institute of Technology (KIT))
- Peter Mörters (Universität Köln)
- Matthias Sperl (Deutsches Zentrum für Luft- und Raumfahrt (DLR) Köln)
This Priority Programme (PP) is devoted to the mathematical analysis of effects and phenomena that emerge from an interplay
between randomness and geometry. Analytical work will be dominant, but simulations, numerical, statistical and modelling
work will also be part of the programme. Many questions of intrinsic mathematical interest will be attacked.
Disciplines like physics, materials science and telecommunication will be crucial sources of problems, motivations,
models and solutions. The main focus will lie on the development of new and
the refinement of existing methods, and on
the creation and analysis of new random spatial models. Goals comprise the rigorous description and analysis of
- emergence of macroscopic phenomena like condensation, percolation, crystallisation;
- geometric functionals of random structures like Minkowski functionals and cluster counts;
- new limiting geometries;
- geometric systems driven by correlated spatial randomness;
- metastability in spatial processes away from equilibrium;
- effects arising from kinetic or geometric constraints;
- new applied spatial random models.
The above questions are fundamental and ubiquitous; this PP will bring substantial new development into various timely directions,
like time-dependent random media, continuous-space modelling, long-range dependence of interactions,
description of entire geometries instead of characteristic quantities, the introduction of spatiality
into mean-field models, and more. The most recent activities in the field will be merged and further
explored, new analytic and modelling paradigms will be developed.
A systematic transfer of questions from the applied sciences into mathematics will be an integral part of this PP.
In this sense, the PP has an interdisciplinary outreach, with a major focus in probability.
The main body of research that will be done in this PP will concentrate on the topics
- Point processes
- Random fields
- Percolation in the continuum
- Random geometric graphs
- Energy-based random point configurations
- Stochastic processes in random media
The decision to set up this PP was taken by the DFG on 27 March 2019.
It is hoped to publish a call for individual projects here during May 2019.
Research within this PP should begin during the year 2020.