7 problems

Chalker–Mehlig conjecture. (i) For any two points $z_1,z_2$ such that $|z_1|<1$, $|z_2|<1$ and $|z_1-z_2|>0$,

Let eGinUE, eGinOE, and eGinSE denote the elliptic Ginibre unitary, orthogonal, and symplectic ensembles, respectively, and let SNH denote the regime of strong non-Hermiticity. The…

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…

Burda et al.'s large-$N$ solution conjecture. These explicit solutions are valid in the limit $N\to\infty$.

Let $G$ be distributed according to the truncated unitary ensemble $\mathrm{TUE}(N,M)$, let $\mathscr{O}_{ii}$ denote its diagonal overlap, and let $\lambda_1,\dots,\lambda_N$ be t…

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…

Let $V_0$ and $V_1^t$ be the initial and perturbed eigenspaces, and let $D(V_0,V_1^t)$ denote their overlap distance. In the perturbative regime $N\gg1$ and $Nt\ll1$, suppose that…