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July 7, 2022


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Probability and Geometry on Groups course, free PDF book by Gabor Pete Technical University of Budapest.

  • 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

Summary on tutorial Probability and Geometry on Groups

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