3 problems

Let $G_N$ be the $N\times N$ real Ginibre matrix, let $\gamma$ vary in a fixed compact subset of $(-\frac{1}{2},\infty)$, and let $x$ vary in a fixed compact subset of $(-1,1)$. Th…

GinOE number variance scaling limits. As $N\to\infty$, the following limits are expected. For fixed $a\in(0,1)$,

Let $X$ be an $N\times N$ real Ginibre matrix, let $A$ be a deterministic matrix, let $\gamma>0$, and define the Hermitian imaginary part by … Write $\sigma_1(\gamma X+A)$ for the…