The Airy line ensemble at the edge of uniform alternating sign matrices

@misc{liao2026airy,
  title = {{The Airy line ensemble at the edge of uniform alternating sign matrices}},
  author = {Yuchen Liao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.20603},
  eprint = {2609.20603},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.20603},
}

TY  - UNPB
TI  - The Airy line ensemble at the edge of uniform alternating sign matrices
AU  - Yuchen Liao
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.20603
UR  - https://arxiv.org/abs/2609.20603
AB  - We prove that the height-level path ensemble of a uniform alternating sign matrix converges to the Airy line ensemble near every interior point of the north-west arctic arc. Under the standard bijection, this is equivalently a limit theorem for the osculating paths of the domain-wall six-vertex model at the ice point. The proof has two main inputs. The integrable input is a new Pfaffian formula for rectangular frozen-corner probabilities, from which we obtain one-point convergence of the top path to the GUE Tracy--Widom distribution. The probabilistic input is an exact resampling law and accompanying bridge estimates for a strictly ordered midpoint encoding of the paths; these yield tightness and the Brownian Gibbs property for every subsequential limit. Aggarwal and Huang's strong characterization then identifies each such limit as the Airy line ensemble.
ER  -