Robust QIE and limits of Anosov representations

One of the key properties of Anosov representations into any real semisimple Lie group $G$, is that they are structurally stable (i.e. small perturbations of an Anosov representation of a hyperbolic group remain Anosov). In this talk, we will provide examples of stable, quasi-isometrically embedded hyperbolic subgroups of $\textup{SL}_n(\mathbb{C})$ (n sufficiently large) which fail to be algebraic limits of Anosov representations, showing that structural stability fails to characterize Anosov representations.