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

@misc{dauvergne2026downthemiddle,
  title = {{Down-the-middle isometries for the Airy and KPZ sheets}},
  author = {Duncan Dauvergne and Fardin Syed},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.26902},
  eprint = {2609.26902},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26902},
}

TY  - UNPB
TI  - Down-the-middle isometries for the Airy and KPZ sheets
AU  - Duncan Dauvergne
AU  - Fardin Syed
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.26902
UR  - https://arxiv.org/abs/2609.26902
AB  - We find a new coupling between the Airy sheet 𝒮 and the Airy line ensemble { 𝒜_n }_n ∈ ℕ, which we call the down-the-middle isometry. In this coupling, the Airy sheet is encoded by last passage values that start at 𝒜_k(0) for some k ∈ ℕ and end on the top line 𝒜_1. Using this coupling, we give a new construction of the (extended) Airy sheet as a scaling limit of Brownian last passage percolation and study coalescence of geodesics in the directed landscape. This coupling extends to discrete polymers and last passage percolation models, as well as to the KPZ line ensemble and KPZ sheet.
ER  -