Actions in the Airy line ensemble and convergence to the Airy sheet
Abstract
Actions in the Airy line ensemble represent distances from an infinitely far object. We characterize the Airy sheet by S(x,.)=Tx(.,1), where Tx 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.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.