KPZ line ensemble convergence conjecture to the Airy line ensemble

For each $t>0$, let $\{\mathfrak{H}^{t}_{n}(x):n\in\mathbb{N},x\in\mathbb{R}\}$ be the KPZ$_t$ line ensemble, and let $\{\mathcal{A}_n(x):n\in\mathbb{N},x\in\mathbb{R}\}$ be the Airy line ensemble. Define the rescaled line ensemble by

$$\mathcal{L}^{t}_n(x)=2^{1/3}\left(\mathfrak{H}^{t}_{n}(x)+\frac{x^2}{2}\right).$$

KPZ line ensemble convergence conjecture. As $t\to\infty$, the line ensemble $\{\mathcal{L}^{t}_n(x)\}$ converges, in the sense of line ensembles, to the Airy line ensemble $\{\mathcal{A}_n(x):n\in\mathbb{N},x\in\mathbb{R}\}$.

The conjecture strengthens the known one-point convergence to the GUE Tracy–Widom distribution and the earlier conjecture for the lowest curve, asserting convergence of the entire KPZ line ensemble. It is a proposed formulation of KPZ universality and remains open in the source.