Stochastische Geometrie/Stochastic Geometry (Summer Semester 2011)
- Lecturer: Prof. Dr. Daniel Hug
- Classes: Lecture (0152600), Problem class (0152700)
- Weekly hours: 4+2
|Lecture:||Monday 11:30-13:00||Z 2|
|Thursday 11:30-13:00||Z 2|
|Problem class:||Wednesday 15:45-17:15||Z 2|
|Lecturer, Problem classes||Prof. Dr. Daniel Hug|
|Office hours: Nach Vereinbarung.|
|Room 2.051 Kollegiengebäude Mathematik (20.30)|
|Email: firstname.lastname@example.org||Problem classes||Andreas Reichenbacher|
|Office hours: Montags, 10:00-11:00 Uhr oder nach Vereinbarung|
|Room 2.008 Kollegiengebäude Mathematik (20.30)|
In Stochastic Geometry mathematical models are developed for describing and analyzing random geometric structures. The course provides an introduction to the foundations of this field which is also highly interesting from an applied point of view.
In the first part, random closed sets and point processes are introduced as basic models. Then specific geometric characteristics of random structures will be developed. It is also planned to include an introduction to random tessellations. Specific topics to be covered include: geometric point processes and random closed sets, stationarity and isotropy, Poisson and related point processes, germ-grain models and Boolean model, specific intrinsic volumes, contact distributions, random tessellations.
Basic concepts of probability theory (including some measure theory), convex geometry and stochastic processes are helpful, but not required.
- I. Molchanov: Statistics of the Boolean Model for Practitioners and Mathematicians, Wiley, 1997.
- J. Ohser, F. Mücklich: Statistical Analysis of Microstructures in Materials Science, Wiley, 2000.
- R. Schneider, W. Weil: Stochastic and Integral Geometry, Springer, 2008.
- D. Stoyan, W. S. Kendall, J. Mecke: Stochastic Geometry and its Applications, Wiley, 1995, 2nd ed.