Actions in the Airy line ensemble and convergence to the Airy sheet (2511.11207v1)

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.