11 problems

Let an Airy line ensemble be a non-intersecting line ensemble with the Brownian Gibbs property, and suppose that after subtracting a parabola its law is stationary. A height shift…

A half-space Gibbsian line ensemble is expected to have a scaling limit called the pinned half-space Airy line ensemble. Locally, the curves are ordered line ensembles with pinning…

Uniform convergence conjecture. The two line ensembles

Airy-type characterization conjecture. Then $\mathcal{L}$ is equal in distribution to the $\mathrm{KPZ}_t$ line ensemble, up to an independent affine shift.

Parabolic rigidity conjecture. As $n\to\infty$, the sequence of functions

Asymptotic gap conjecture. Almost surely as $n\to\infty$,

Logarithmic-shift BK conjecture. The KPZ line ensemble satisfies a form of the BK inequality with a shift that is logarithmic in the size of the interval over which the first curve…

The KPZ line ensemble is a collection of random curves associated with the KPZ equation, and the fundamental solution is the solution kernel that propagates initial data for that e…

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…

Let $\mu_{n,T}^{\mathfrak{f}}$ denote the line-ensemble measure with Lebesgue-free boundary conditions, and let $\mu_{\infty}^{\mathfrak{0}}$ be the limiting measure obtained for z…

Let $\mathbb{P}_{HL}^{r,t}$ be the Hall–Littlewood measure on plane partitions. Fix $T>0$ and impose … For $\tau\in\mathbb{R}$, define $\Xi^\tau$ by the normalization displayed in…