Probability on Graphs

What it is about

You will learn stochastic models on graphs, e.g. Random Walks, percolation and random graphs. In the end you will be able to analyse Random Walks on networks, use the connection to electrical networks to show recurrence/transience, and understand phase transitions and random spanning trees.

What you will be able to do

• Analyze Random Walks on networks
• Use the connection between Random Walks and electrical networks to show recurrence/transience
• Familiarity with random spanning trees
• Recognize phase transitions in percolation and describe behavior in subcritical, critical and supercritical phases

What the module consists of

• VorlesungPresentation of content with examples and discussion; conveys the theoretical foundations
• ÜbungDeepening through problem sheets and solutions; independent verification of understanding

Teaching method

• VorlesungExplanation of topics in lectures with demonstrative examples and discussion
• ÜbungssitzungenWorking on problem sheets and checking own progress through solutions