Probability and Geometry on Groups

• 1 Basic examples of random walks
• 2 Free groups and presentations
• 3 The asymptotic geometry of groups
• 4 Nilpotent and solvable groups
• 5 Isoperimetric inequalities
• 6 Random walks, discrete potential theory, martingales
• 7 Cheeger constant and spectral gap
• 8 Isoperimetric inequalities and return probabilities in general
• 9 Speed, entropy, Liouville property, Poisson boundary
• 10 Growth of groups, of harmonic functions and of random walks
• 11 Harmonic Dirichlet functions and Uniform Spanning Forests
• 12 Percolation theory
• 13 Further spatial models
• 14 Local approximations to Cayley graphs
• 15 Some more exotic groups
• 16 Quasi-isometric rigidity and embeddings

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