Boolean models

• Applicants: Professor Dr. Daniel Hug; Professor Dr. Günter Last
• Subject Area: Mathematics
• Term: from 2011 to 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 173504944

The general aim of this project is the further analysis of geometric properties of the Boolean model. The statistical analysis of a Boolean model Z is getting more and more involved in higher dimensions, and in particular if invariance assumptions are relaxed. For instance, the motion invariant intrinsic volumes and their local counterparts, the (covariant) curvature measures, are clearly not sufficient anymore to obtain complete information on the directional distributions of the underlying Poisson particle process X. A major purpose of this project is to use various recent geometric tools and to develop new ones in order to gain deeper insight into the probabilistic properties of Z and their dependence on the distribution of the particle process X.

• DFG Programme: Research Units
• Subproject of: FOR 1548: Geometry and Physics of Spatial Random Systems