Down-the-middle isometries for the Airy and KPZ sheets

Duncan Dauvergne, Fardin Syed

We find a new coupling between the Airy sheet $\mathcal{S}$ and the Airy line ensemble $\{{\mathcal{A}}_n{\}}_{n\in \mathbb{N}}$, which we call the down-the-middle isometry. In this…