Ergodicity of the Airy line ensemble

Abstract

In this paper, we establish the ergodicity of the Airy line ensemble. This shows that it is the only candidate for Conjecture 3.2 in [3], regarding the classification of ergodic line ensembles satisfying a certain Brownian Gibbs property after a parabolic shift.

argument for Proposition 1.13 is revised, the structure of the introduction is rearranged