Random subgroups of linear groups are free

TL;DR

This paper proves that in any finitely generated non virtually solvable linear group, multiple independent random walks will almost surely generate a free subgroup, highlighting a probabilistic structure within these groups.

Contribution

It establishes that random walks in such groups almost surely produce free subgroups, extending understanding of their probabilistic algebraic properties.

Findings

Random walks generate free subgroups with high probability.

The result applies to an exponential number of independent random walks.

Free subgroup generation is almost certain in these groups.

Abstract

We show that on an arbitrary finitely generated non virtually solvable linear group, any two independent random walks will eventually generate a free subgroup. In fact, this will hold for an exponential number of independent random walks.