Generic thinness in finitely generated subgroups of ${\text{SL}}_n(\mathbb{Z})$

Elena Fuchs, Igor Rivin

We show that for any $n\ge 2$, two elements selected uniformly at random from a \emph{symmetrized} Euclidean ball of radius $X$ in ${\text{SL}}_n(\mathbb{Z})$ will generate a thin…