7 problems

Let $\mathsf{Ht}_\mathcal N$ be the random height function of the model at scale $\mathcal N$, let $\mathbb E[\mathsf{Ht}_\mathcal N]$ be its expectation, let $\pounds$ denote the…

Let $\beta>0$, and let the Gaussian beta ensemble G$\beta$E have joint density … Let $t^n_{k,\beta}$ be its $k$-th smallest gap. Small-gap conjecture. There exists a constant…

Exotic edge-operator conjecture. After the appropriate scaling, $T_n$ converges to the random operator $\mathcal{S}_{\beta,k}$. The source presents this as a conjecture and refers…

Witte–Forrester conjecture. For even $l\leq 2$,

Large-argument hypergeometric asymptotic conjecture. For large values of the arguments $\{s_j\}_{j=0,\dots,n}$, the generalized hypergeometric function has the asymptotic form give…

Hard-edge gap-ratio asymptotic conjecture. As $s\to\infty$,

Let $V_{d+1}(x)$ be any potential of degree $d+1$, and let ${\widetilde{\epsilon}}_i$ be the occupation numbers on the cycles ${\widetilde{{\cal A}}}_i$, for $i=1,\ldots,d$. Here…