8 problems

Let $A$ and $B$ be independently chosen from the real Gaussian orthogonal ensemble $GOE_n^{\mathbb R}$, consisting of real symmetric $n\times n$ matrices with the standard GOE dist…

Let $\lambda\in\mathbb C$ be an affine coordinate on $\mathbb{CP}^1$, let … and let $G(q)$ denote the logarithmic energy of the elliptic law with elliptic parameter $\sqrt q$. Let…

Fix a real-valued probability distribution $\mu$ with mean zero and finite moments, and a complex-valued probability distribution $\nu$ with mean zero, unit variance, finite moment…

For each $n$, let $\mathcal P_n^{GUE}(\theta,\phi)$ denote the level-crossing density for a pencil of independent GUE matrices, expressed in spherical coordinates $(\theta,\phi)$ o…

Consider real matrix ensembles with additional linear constraints, including real symmetric or other structured real matrices. Let $\rho(\lambda)\,dx\,dy$ denote an absolutely cont…

Let $A_n=(a_{ij})$ and $B_n=(b_{ij})$ be independent real $n\times n$ matrices with i.i.d. entries satisfying … and assume a standard moment condition strong enough to imply the ci…

Let $A_n$ and $B_n$ be independent GOE matrices, and write the normalized complex Gaussian pencil as $\widehat C_n(\lambda)=(A_n+\lambda B_n)/\sqrt{n(1+|\lambda|^2)}$. Its entry ps…

Consider the two-photon Rabi model and its numerically obtained energy spectrum. Emary and Bishop identified a class of level crossings associated with exact solutions expressible…