Contents

1 Introduction
1.1 Discrete representations
1.2 Models of randomness

2 Random finite presentations
2.1 The density model
2.2 The few relators model
2.3 1-relator groups
2.4 Rigidity properties
2.5 Nilpotent groups

3 Random subgroups
3.1 Stallings graph of a subgroup
3.2 The central tree property and its consequences
3.3 Random Stallings graphs
3.4 Whitehead minimality
3.5 Random subgroups of non-free groups

4 Non-uniform distributions
4.1 Prefix-heavy distributions
4.2 Markovian automata