Random groups and nonarchimedean lattices

2013/08/10 by Sylvain Barre, Barre, Sylvain, Mikael Pichot +1
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1308.2315

arxiv created 2014/09/24 · arxiv updated 2014/09/26

Abstract

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.

Related

• Random group cobordisms of rank 7/4
• Property (T) in random quotients of hyperbolic groups at densities above 1/3
• On random presentations with fixed relator length
• Linear representations of random groups
• Random groups are not left-orderable