Ergodicity of the Airy line ensemble
  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. 
Ivan Corwin and Xin Sun
math.PR math-ph math.MP