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Spatial Stochastics and Stochastic Geometry


Spatial stochastics developes mathematical methods for the analysis, statistical investigation, and simulation of random spatial structures and phenomena. It has, for example, applications in physics, materials science, medicine, or mobile telecommunications.

Basic models of spatial stochastics are random measures, random (e.g., Gaussian) fields, (geometric) point processes and random tessellations. An essential part of the research is concerned with random point processes and random measures. In this context, for instance, invariance properties of the characteristics of stationary random measures are explored on homogeneous or on more general spaces which are subject to a group action. Stochastic geometry constitutes a central part of the research area. The focus of interest is the modeling and analysis of distributional properties of point processes, of convex (and more general) sets as well as of geometrically defined measures.

Some members of the research unit also deal with convex and integral geometry which is a strong pillar of stochastic geometry. Here curvature and support measures of compact sets, additive functionals (such as tensor valuations) and related integral-geometric formulas are explored.

For some further motivation and information about lectures on topics of the research group visit Courses on Spatial Stochastics.

Selected Publications

... of the DFG research unit


Most guests of our group give talks in one of our seminars. For a list of guests of any of the previous semesters we therefore refer to the meetings of the Stochastic Geometry group.