10 problems

Consider non-Hermitian random matrices with independent and identically distributed entries. Their microscopic eigenvalue statistics in the bulk and at the soft edge exhibit the sa…

For non-Hermitian random matrices, consider local bulk statistics of complex eigenvalues away from spectral edges, symmetry axes, and symmetry points. A universality class is a dis…

Universality conjecture for class A parametric covariance. For models of class A with such global, diffusive, stationary and isotropic dynamics,

Let $f_{\beta=4}(z)$ be the GSE edge-profile function … Here class $\mathbf{AII}^{\dagger}$ denotes the symmetry class of complex quaternion matrices. Kuramoto's universal edge-pro…

Let $X_N$ be an $N\times N$ non-Gaussian random matrix from the interpolating ensemble generated by … where $G_N$ is a Ginibre matrix, $T$ denotes transpose, and the symmetry param…

Consider the complex Ginibre ensemble (class A), the ensemble of complex symmetric matrices (class $\mathrm{AI}^{\dagger}$), and the ensemble of $2N$-dimensional complex self-dual…

Consider the 38 symmetry classes of non-Hermitian random matrices and local level-spacing statistics in the bulk of their spectra. Hamazaki et al. conjecture. Among all 38 classes,…

Let a Markovian open quantum system be described by a non-Hermitian Hamiltonian and hence have generally complex spectral data. Grobe–Haake–Sommers conjecture. Its spectral propert…

Let $X$ be a random matrix satisfying the assumptions of Theorem, and let $T$ be its Schur form. Define $Y=n|t_{12}|^2$, where $t_{12}$ is the relevant off-diagonal entry of $T$, a…

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…