Workgroup Stochastic Geometry
Stochastic geometry is concerned with the mathematical modeling and the analysis of random spatial geometric structures. Basic examples of such structures are Voronoi mosaics generated by point processes, random systems of overlapping and non-overlapping convex bodies (Boolean models, systems of hard spheres, packings) or the excursion or level sets of Gaussian random fields. Stochastic geometry uses and developes a wide range of mathematical techniques from convex and integral geometry, probability theory, fractal geometry and geometric measure theory.
There are many interesting applications of stochastic geometry, for instance in physics (physical properties of disordered systems), materials science (statistical modeling of microstructures), medicine (stereological analysis of sections of spatial fiber processes) astronomy (distribution of galaxies) and mobile telecommunications (hierarchical networks).
The research group in Karlsruhe is particularly concerned with projects related to random mosaics, Boolean models, curvature measures and their applications, random polytopes, contact distributions of random sets and geometric point processes.