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arXiv · 2511.11207

Actions in the Airy line ensemble and convergence to the Airy sheet

Balint Virag·Xuan Wu
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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.

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Balint Virag, Xuan Wu. 2025-11-14. Actions in the Airy line ensemble and convergence to the Airy sheet. https://arxiv.org/abs/2511.11207

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