12 problems

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

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…

Linear $F_2$-form conjecture. Every rational linear combination of finite minors of $(u_{jk})_{j,k=0}^\infty$ is a linear $F_2$-form of order

Consider the directed polymer in the intermediate disorder regime, with $b2=b2_n=n^{-b1}$ and $b1<1/4$. Let $c7$ denote the exponent governing free-energy fluctuations, and let the…

Let $u_{jk}$ be the functions introduced by the recursive algorithm, and let $F$ denote the Tracy--Widom distribution. For positive integers $m$ and index sets $j_1,\ldots,j_m$ and…

Let $F$ denote the Tracy--Widom distribution, and let $\widetilde F_m$, $F_m$, $F_m^P$, $F_m^D$, and $F_m^*$ be the expansion coefficients introduced in the paper. For…

Let $q\in(0,1)$ and let $n$ be the parameter determining the one-species jump rates. Define … Consider the type $D$ ASEP with parameters $(2,0)$ and $(3,0)$ on the infinite lattice…

Consider the sparse graph model of Corollary, with sparsity parameter $q$ and largest edge eigenvalue. In the regime $q\ll n^{1/6}$, the source notes that the limiting distribution…

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…