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Random groups (following Misha Gromov, \(\dots\)). (Groupes aléatoires (d’après Misha Gromov, \(\dots\)).) (French) Zbl 1134.20306
Séminaire Bourbaki. Volume 2002/2003. Exposés 909–923. Paris: Société Mathématique de France (ISBN 2-85629-156-2/pbk). Astérisque 294, 173-204, Exp. No. 916 (2004).
Summary: What are the properties of a finitely presented group “chosen at random”? The answer to this question depends on the method of sorting a group at random. One could fix the number \(n\) of generators and choose \(p\) relators at random among words of length \(L\), and then let \(L\) go to infinity. One could also choose some finite graph, label its edges randomly by generators, and consider the group generated by these generators subject to the relations read on the cycles of the graph. In this talk, I would like to introduce the reader to some works of M. Gromov answering this kind of questions. These methods produce examples of finitely presented groups with surprising properties.
For the entire collection see [Zbl 1052.00010].

MSC:
20F65 Geometric group theory
20F67 Hyperbolic groups and nonpositively curved groups
20F05 Generators, relations, and presentations of groups
20P05 Probabilistic methods in group theory
60G50 Sums of independent random variables; random walks
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