8 problems

Asymptotic independence conjecture. For every $x,y\in\mathbb{R}$,

Tracy–Widom and proportion conjecture. The distribution of $\lambda_\pm(G)$, normalized in this way, converges as $N\to\infty$ to the $\beta=1$ Tracy–Widom distribution rather than…

Let $T_h$ be the limiting passage time defined by the preceding convergence result, let $x\in\mathbb R$ be fixed, and let $\mathcal A(x)$ denote the stationary Airy process. Airy-p…

Borot–Eynard–Majumdar–Nadal conjecture. The left-tail asymptotic expansion is

Higher-eigenvalue Airy-process conjecture. For any fixed $k$, as $n\to\infty$, the tuple $(\alpha_{n,1},\ldots,\alpha_{n,k})$ converges in distribution to the top $k$ points of the…

Let $G_n$ be the hexagonal-lattice rhombus with $2n-1$ levels, and let $H_n$ be its weighted adjacency operator. In the i.i.d. model, all edge weights are independent copies of a n…

Rumanov's boundary-value conjecture. The function above determines the solution of the boundary-value problem for the Bloemendal–Virág equation if $(q_2,\alpha)$ satisfies

Let $(a_n)$ be a nondecreasing sequence with $a_n\to\infty$ as $n\to\infty$, and let $X^{(n)}_{i,j}$ denote the relevant entry of the random rectangular Young tableau. Write $TW$ f…