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(Ehemalige) Arbeitsgruppe Konvexe Geometrie

Sekretariat
Allianz-Gebäude (05.20)
Zimmer 4A-16

Adresse
Institut für Algebra und Geometrie
Universität Karlsruhe (TH)
Kaiserstr. 89-93
76133 Karlsruhe

Öffnungszeiten:
Montag bis Freitag, 9:15 Uhr bis 11:15 Uhr

Tel.: ++49 721 608 4 3943

Fax.: ++49 721 608 4 6909

Stochastische Geometrie/Stochastic Geometry (Sommersemester 2011)

Dozent: 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
Dozenten
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

lectures more lectures


Exercises

Sheet 1 Solutions for Sheet 1 Sheet 2 Solutions for Sheet 2 Sheet 3 Solutions for Sheet 3 Sheet 4 Solutions for Sheet 4 Sheet 5 Solutions for Sheet 5 Sheet 6 Solutions for Sheet 6 Sheet 7 Sheet 8 Solutions for Sheet 8 Sheet 9 Sheet 10 Solutions for Sheet 10 Sheet 11 Solutions for Sheet 11

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.