This course provides lectures on stat-of-the-art topics by faculty members invited from overseas universities.
Introduction to Spatial Stochastic Modeling: Random Graphs, Point Processes and Stochastic Geometry
The goal of the course is to provide quick access to some mathematical tools useful in the modeling and analysis of modern communication networks, including social, transportation, wireless networks, etc. Historically, these tools might have been developed and belong to different theories, as the theory of percolation, random graphs, point processes and stochastic geometry. Here, we present them in one course that gives us an opportunity to observe some similarities and even some fundamental relations between apparently different concepts, e.g. formalization of the notion of the typical node in random graphs via unimodularity and the mass transport principle for point processes, or a similar role the Galton-Watson tree and Poisson point process are playing in the two aforementioned settings.
Students should be able to discuss on the topics.
state-of-the-art topics in information science and technology
✔ Specialist skills | ✔ Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Specified in the class
Course schedule | Required learning | |
---|---|---|
Class 1 | Bond Percolation Model | Specified in the class |
Class 2 | Galton-Watson Tree | Specified in the class |
Class 3 | Erdos-Renyi Graph I - Emergence of the Giant Component | Specified in the class |
Class 4 | Configuration Model | Specified in the class |
Class 5 | Unimodular Graphs | Specified in the class |
Class 6 | Erdos-Renyi Graph II - Emergence of the Connectivity | Specified in the class |
Class 7 | Poisson Point Process | Specified in the class |
Class 8 | Palm Theory | Specified in the class |
Class 9 | Hard Core Models | Specified in the class |
Class 10 | Stationary Framework for Point Processes and Mass Transport Principle | Specified in the class |
Class 11 | Stationary Voronoi Tessellation | Specified in the class |
Class 12 | Ergodicity and Point-shift Invariance | Specified in the class |
Class 13 | Random Closed Sets | Specified in the class |
Class 14 | Boolean Model I - Coverage Properties | Specified in the class |
Class 15 | Boolean Model II - Connectivity (Continuum Percolation) | Specified in the class |
None. The notes will be sent after each lesson to students who follow the lecture.
1. M. Draief & L. Massoulie. Epidemics and Rumours in Complex Networks. Cambridge, 2010.
2. R. van der Hofstad. Random Graphs and Complex Networks. Cambridge, 2017 (available also on
http://www.win.tue.nl/~rhofstad/publications.html).
3. D. J. Daley & D. Vere-Jones. An Introduction to the Theory of Point Processes, Volume II: General Theory and Structure.
Springer, 2008.
4. S. N. Chiu, D. Stoyan, W. S. Kendall & J. Mecke. Stochastic Geometry and its Applications. Wiley, 2013.
5. G. R. Grimmett. Percolation. Springer, 1999.
A take-home exam at the end of the course
Specified in the class