Seminar: Random graphs
Winter semester 2021/22
Prof. Dr. Silke Rolles
- Time and place: Weekly, every Thursday 14:15-15:45 in MI 00.07.014.
- First talk: Thursday, 21 October 2021
- Prerequisites: Einführung in die Wahrscheinlichkeitstheorie und Statistik (MA0009).
- Content: Random graphs are used as probabilistic models for complex networks. In the seminar we want to study several well know random graph models including the Erdös-Renyi random graph and the preferential attachment model. In particular, we will study the phase transition for the Erdös-Renyi random graph. During the seminar, we will learn important tools in the study of stochastic processes including couplings, stochastic order, probabilistic bounds and branching processes.
- Literature:
- R. van der Hofstad. Random Graphs and Complex Networks. Volume 1. Cambridge Series in Statistical and Probabilistic Mathematics (2017). Homepage of the book
- Manfred Lehn: Wie halte ich einen Seminarvortrag
- R. van der Hofstad. Random Graphs and Complex Networks. Volume 1. Cambridge Series in Statistical and Probabilistic Mathematics (2017). Homepage of the book
- Bachelor or Master thesis: It is possible to write a Bachelor or Master thesis on a related topic.
- Talks: Every talk is based on parts of a chapter of the book by Remco van der Hofstad.
- 1.1-1.7 Introduction
- 1.8-1.9 Introduction, 2.1-2.3 Probabilistic Method
- 2.4-2.6 Probabilistic Method
- 3.1-3.4 Branching Processes
- 3.5-3.7 Branching Processes
- Phase transition for the Erdös-Renyi random graph, part 1
- Phase transition for the Erdös-Renyi random graph, part 2
- 5.1-5.2 Erdös-Renyi random graph revisited
- 5.3-5.4 Erdös-Renyi random graph, Intermezzo: Back to real-world networks
- 6.1-6.4 Generalized random graphs
- 6.5-6.8 Generalized random graphs
- 8.1-8.5 Preferential attachment models