Stochastische Geometrie/Stochastic Geometry (Sommersemester 2011)
- Dozent*in: Prof. Dr. Daniel Hug
- Veranstaltungen: Vorlesung (0152600), Übung (0152700)
- Semesterwochenstunden: 4+2
| Termine | ||
|---|---|---|
| Vorlesung: | Montag 11:30-13:00 | Z 2 |
| Donnerstag 11:30-13:00 | Z 2 | |
| Übung: | Mittwoch 15:45-17:15 | Z 2 |
| Lehrende | ||
|---|---|---|
| Dozent, Übungsleiter | Prof. Dr. Daniel Hug | |
| Sprechstunde: Nach Vereinbarung. | ||
| Zimmer 2.051 Kollegiengebäude Mathematik (20.30) | ||
| Email: daniel.hug@kit.edu | Übungsleiter | Dr. Andreas Reichenbacher |
| Sprechstunde: Montags, 10:00-11:00 Uhr oder nach Vereinbarung | ||
| Zimmer 2.008 Kollegiengebäude Mathematik (20.30) | ||
| Email: andreas.reichenbacher@kit.edu | ||
Course description
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.
Prerequisites
Basic concepts of probability theory (including some measure theory), convex geometry and stochastic processes are helpful, but not required.
Lectures
Exercises
References
- 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.