10 problems

Let $n(r)$ be the number of zeros of the planar Gaussian analytic function $\mathbf g$ in the disk $D(0,r)$. Sodin's deviation conjecture. As $r\to\infty$, … This predicts the loga…

Let $n(r)$ denote the number of zeros of a planar or hyperbolic Gaussian analytic function in the disk of radius $r$ centered at the origin, with $r<1$ in the hyperbolic case. Pere…

Let $A_k$, for $k\geq 0$, be independent $n\times n$ matrices whose entries are independent standard complex Gaussian random variables. The zeros in the unit disk of the determinan…

Let $N_q$ denote the number of zeros under consideration, and let … be the conditional hole probability, with $a^2>0$. Forrester–Ipsen conjecture. As $q$ approaches $1$, the leadin…

Let $\boldsymbol{\zeta}$ denote the Riemann zeta function, let $\omega$ be uniform on $[0,1]$, and let $\zeta_2$ be the stochastic zeta function associated with the…

Stable-domain conjecture. Coefficients from a stable domain of attraction should lead to a different limiting mean density function.

Let $z_0$ be a point in the bulk of the pseudospectrum, and let $\tilde G_{z_0}$ be the determinant of the $J\times J$ matrix of independent Gaussian analytic functions arising as…

Microscopic zeta-function convergence conjecture. In law, uniformly for $z$ on every compact subset of $\mathbb C$,

Let $f$ be the Gaussian entire function, let $K\subset\mathbb{C}$ be a connected compact set with non-empty interior, and let $rK$ denote the homothety of $K$ by $r$. Write … and l…

Let $\Pi_\mathrm{L}$ be any transitive point process of intensity $1$, let $\Pi_\mathrm{GAF}$ be the zero set of a Gaussian analytic function with intensity $1$, and let…