# Spatial Stochastics and Stochastic Geometry

### Members

Tillmann Bühler

Mikhail Chebunin

Daniel Hug

Maxim Glyzhev

Günter Last

Franz Nestmann

Dominik Pabst

Babette Picker

Steffen Winter

### Summary

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.

### Projects and fields of research

- DFG priority programme 2265 Random Geometric Systems
- Work group Point Processes and Random Measures
- Work group Stochastic Geometry
- Work group Convex- and Integral Geometry
- DFG-Project Scaling of curvature measures and the modified Weyl-Berry conjecture
- DFG reseach unit
**Geometry and Physics of Spatial Random Systems**(until 2018; Summary of the Final Report (in German)) - DFG-GACR Project Curvature Measures and Integral Geometry (until 2013)

### Research Seminar of the group

summer term 2023 | winter term 2022/2023 | summer term 2022 | ... of former semesters |

### Selected Publications

... of the DFG research unit |

### Guests

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.