8 problems

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 $q$ and $\kappa$ be the model parameters, let $\mathcal{F}_n^s(0)$ be the orthogonal functions appearing in the barcode kernel, and let $\mathcal{K}^{\mathrm{barcode}}(s,t)$ be…

Let $K^{\mathrm{barcode}}_{(L)}(s,t)$ be the pre-limit barcode kernel for $s,t\in\mathbb{Z}$, and let $q$ be the model parameter. Barcode-kernel limit conjecture. For all…

For $t\in\mathbb{Z}$ and $M\in\mathbb{Z}$, define the two truncation limits $\rho_0(t)$ and $\rho_1(t)$ by the displayed sums over $n\in\frac12\mathbb{Z}_{\ge0}$. Let…

Let $(\mathsf{t},\mathsf{x})$ be a macroscopic point in the waterfall region $\mathcal{W}$, and let $q$ and $\kappa$ be the model parameters. Let…

Universal Edge Fluctuation Conjecture. Under suitable assumptions on the convergence of $G_n$, all scaling limits of the determinantal point processes at the frozen boundary are gi…

Determinantal representation conjecture. The unique smooth normalized solution $\varphi$ may be represented as a limit in $L^{1}(X)$:

Let $cmathbb{S}^d$ be the unit sphere and let $n=cpi_L$. Let $K$ be an isotropic kernel producing $n$ points through its determinantal point process, and let $E_s(x)$ denote the Ri…