Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Liao, Yuchen
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213592309