  We 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 include for example a
"density model" for groups of intermediate rank. The main novelty is the higher
rank nature of the random groups. They are randomization of certain families of
lattices in algebraic groups (of rank 2) over local fields.
