Applications of Almost Stationarity I: Quantitative Growth of Injectivity Radius and Stück-Zimmer Theorem

Fraczyk and Gelander proved in \cite{FG} that for any simple Lie group $G$ of high rank and for every non-lattice discrete subgroup $Γ\leq G$, the injectivity radius of points in $G/Γ$ is unbounded, resolving a conjecture of Margulis. In this work we obtain an explicit lower bound on the growth ra