Overlaps, Eigenvalue Gaps, and Pseudospectrum under real Ginibre and Absolutely Continuous Perturbations

Jess Banks, Jorge Garza Vargas, Archit Kulkarni +1

Let $G_n$ be an $n\times n$ matrix with real i.i.d. $N(0,1/n)$ entries, let $A$ be a real $n\times n$ matrix with $\Vert A\Vert \le 1$, and let $\gamma \in (0,1)$. We show that with p…