6 problems

Uniqueness conjecture. For each $T>0$, $H(t)$ has a unique point of maximum in $[-T,T]$ almost surely.

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 $T_h$ 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…

Let $D$ be the space of admissible directed-landscape environments, let $I$ be the associated rate function, and let $Q$ be the Dirichlet energy of a function…

Let $\mathcal{L} = (\mathcal{L}_1, \mathcal{L}_2, \ldots)$ be a line ensemble such that $\mathcal{L}(x)+x^2$ is stationary under deterministic horizontal shifts, $\mathcal{L}$ has…

Fix $\theta,r>0$ and let $\tilde{f}_N^{LG}$ be the random continuous function from Definition 2. Then, as $N\to\infty$, the random functions $\tilde{f}_N^{LG}$ converge weakly in…