11 problems

Consider the complex deformed Ginibre ensemble $H=A_0+H_0$, with limiting spectral support $D$ and bulk $D^{\mathrm{o}}$. Let $p_k(z_1,\ldots,z_k)$ denote the $k$th correlation fun…

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…

Diagonal-overlap distribution conjecture. The distribution of diagonal overlaps is the same in the bulk and at the edge of GinOE and GinUE, but is essentially different in the depl…

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…

Let $X$ be a real Ginibre matrix and let $z\in\mathbb C$. Write $\sigma_1(X-z)$ for the smallest singular value of the shifted matrix, and let $C>0$ be a constant. Shifted real Gin…

Let $D_{11}^{(N,k)}$ and $D_{12}^{(N,k)}$ denote the conditional overlaps for the complex Ginibre ensemble, and let $D_{11}^{(bulk,k)}$ and $D_{12}^{(bulk,k)}$ be their bulk scalin…

The JLM law. For $R\to\infty$, after taking the number of particles $N$ to infinity, the probability of this event satisfies

Consider a Ginibre matrix conditioned to have $k\sim\alpha n$ real eigenvalues, with macroscopic minimizer ${\mu}_{\alpha}=\alpha \mu^{R}_{\alpha}+(1-\alpha)\mu^{C}_{\alpha}$ for t…

Let $G_1,\ldots,G_s$ be independent random Ginibre matrices, and let $G$ be a given random Ginibre matrix. Write $G_1G_2\cdots G_s$ for their product and $G^s$ for the $s$-th power…

The chiral Gaussian two-matrix ensemble of real asymmetric matrices depends on a non-Hermiticity parameter … kernel to the … kernel as well. This conjecture proposes an extension o…