## Probability on graphs, summer term 2019/2020

### Summary of lectures

- February 25: introduction, G(n,p) and G(n,m) models, threshold functions, threshold for containing triangles, Harris' inequality
- March 3: threshold for containing general subgraphs, Janson's inequalities, large deviations for subgraph counts
- March 10: limiting Poisson distribution of subgraph counts at the threshold, threshold for connectivity
- March 17: threshold for connectivity (continued), sharp thresholds (Friedgut-Kalai's and Friedgut's theorem)
- March 24: the emergence of the giant component, properties of branching processes

### Problem sets

### Literature