RANDOM GROUPS AND NONARCHIMEDEAN LATTICES

International audienceWe consider models of random groups in which the typical group is of intermediate rank (in particular, it is not hyperbolic). These models are parallel to M. Gromov's well-known constructions and in-clude for example a "density model" for groups of intermediate rank. The main novelty is the higher rank nature of the random groups. They are randomizations of certain families of lattices in algebraic groups (of rank 2) over local fields. This paper introduces models of random groups "of higher rank". The construction, basic properties, and applications are detailed in 1 to 7 be-low, which we now summarize. The construction (see 1) is rather general. If Γ ′ is a group which acts properly on a simply connected complex X ′ of dimension 2 with