10 problems

Strong non-Hermiticity scaling conjecture. For $cmu<1$, the $cmu$-dependence of the strong-non-Hermiticity microscopic spectral density can be restored by replacing

Let $f(\lambda)=(2\pi)^{-1}|1-e^{i\lambda}|^{2r}$ and let $\mathcal{F}_r(g)$ be the class of spectral densities defined in the source. For each $r\in\mathbb{N}$, consider the BLUE…

Assume that $a_n=1/2$ for all $n$ and, up to sufficiently rapidly decaying terms, $b_n=\kappa n^{-\varrho}$, where $\varrho<2$ and $\kappa>0$. Let $\tau(\lambda)$ denote the spectr…

Let $G$ be an Archimedean, semisimple, almost-simple and simply connected group, let $\Gamma_1$ be an arithmetic lattice, and let $(\Gamma_N)$ be a sequence of congruence subgroups…

Let a sequence of congruence subgroups be equipped with the Weak Injective Radius Property, the General Density Hypothesis, and the Spherical Density Hypothesis as defined in the s…

Let $G$ be a real, semisimple, almost-simple and simply connected Lie group, let $\Gamma_1$ be a cocompact arithmetic lattice of $G$, and let $(\Gamma_N)$ be a sequence of finite-i…

Let $\rho_{\rm lin}(\lambda,q)$ be the spectral density of the ensemble of $N\times N$ bi-diagonal symmetric random Bernoulli matrices with the Poissonian distribution of nonzero m…

Consider invariant ensembles associated with polynomial potentials $V(x)$ of arbitrary odd degree, possibly with multiple wells, in semi-confining regimes. Let $\rho$ denote a stat…

Askey–Wimp–Kerov stationary-density conjecture. The stationary density for a large system is again given by the Askey–Wimp–Kerov distribution $\rho_c$ for the parameter range

Let $\mathbf{X}$ be a non-Hermitian random matrix model whose mean spectral density is rotationally symmetric around zero. For each centered circular component $R=R_{\textrm{b}}$ o…