Stochastic networks II
Lecturer
Prof. Dr. Volker Schmidt
Exercises
Dipl-Math. Christian Hirsch
Time and place
Lecture
Monday, 8-10 (HeHo 18, Room 220)
Exercise session
Tuesday, 16-18 (HeHo 18, Room 20)
On thursday, July 26 you have the possibility to view your corrected exam from 13:30 to 14:30 in room 2.02, HeHo 22
The intended language of the lecture will be English. However if students unanimously express the wish that the lecture be held in German, this will also be possible.
Type
2 hours lecture + 2 hours exercises
Credit points: 6
Prerequisites
Probability Calculus
Intended Audience
Master students in "Mathematik", "Wirtschaftsmathematik" and "Mathematische Biometrie"; Master students in Finance
Bachelor students in "Mathematik", "Wirtschaftsmathematik" and "Mathematische Biometrie" are also encouraged to participate: An accreditation as supplementary module ("Zusatzmodul") is possible
Contents
This cycle of lectures continues the course stochastic networks offered in winter term 2011/12. While the latter predominantly considered percolation properties of infinite lattice-type networks, the focus of the current lecture cycle is clearly on properties of continuous random spatial networks. In the few cases where results from the previous semester are needed, these will be recalled in class. Therefore the only prerequisite is a basic interest in the stochastic modeling of network systems (which has applications - for instance - in materials science, biology and telecommunications).
We plan to provide a survey on the following spatial stochastic network models
- Boolean model; in particular, coverage and connectivity properties in bounded sampling windows
- Random tessellations such as Poisson-Voronoi and Cox-Voronoi tessellation
- Minimal spanning forest; in particular connectivity of the two-dimensional model and related graphs
- Connectivity and percolation of graphs based on shot-noise intensity fields
- If time allows, also first-passage models on geometric graphs could be considered
Requirements and Exam
Active participation in the exercise classes is a prerequisite for admission to the final exam. All students who want to participate in the exam and who have participated actively in the exercise classes are kindly asked to register for the 'Vorleistung' in the LSF-'Hochschulportal'.
The final exam will be held on Saturday, July 21, 2012.
The exam takes place 9:00-11:00 in room H9 (main university building). Please be there 10 minutes in advance so that we can start on time. Participants may bring one handwritten A4 sheet (both sides) containing useful results from the lecture and exercise classes. Copies and printouts are not allowed.
On thursday, July 26 you have the possibility to view your corrected exam from 13:30 to 14:30 in room 2.02, HeHo 22
Problem sets
solution sketches for selected problems
Lecture Notes
We provide preliminary notes (in German) for stochastic networks.
Literature
- Baccelli and Błaszczyszyn. Stochastic Geometry and Wireless Networks, Volume I - Theory, 2009
- Baccelli and Błaszczyszyn. Stochastic Geometry and Wireless Networks, Volume II - Applications, 2009.
- Franceschetti and Meester. Random Networks for Communication. From Statistical Physics to Information Systems. Cambridge University Press, 2007
- Meester and Roy: Continuum percolation. Cambridge University Press, 1996
- Penrose. Random Geometric Graphs. Oxford University Press, 2007.
- Voss. Spatial Stochastic Network Models, 2010