Actions in the Airy line ensemble and convergence to the Airy sheet
Probability
2025-11-17 v1 Mathematical Physics
math.MP
Abstract
Actions in the Airy line ensemble represent distances from an infinitely far object. We characterize the Airy sheet by S(x,.)=T^x(.,1), where T^x is the unique action in the Airy line ensemble satisfying a growth condition depending on x. This provides a new simple framework for establishing convergence to the Airy sheet. We present simple conceptual proofs of such results in the case of Brownian last passage, the O'Connell-Yor semidiscrete polymer, the log-gamma polymer and the KPZ equation.
Cite
@article{arxiv.2511.11207,
title = {Actions in the Airy line ensemble and convergence to the Airy sheet},
author = {Balint Virag and Xuan Wu},
journal= {arXiv preprint arXiv:2511.11207},
year = {2025}
}
Comments
48 pages