Ergodicity of the Airy line ensemble

Ivan Corwin (Columbia University, Clay Mathematics Institute, Massachusetts Institute of Technology)
Xin Sun (Massachusetts Institute of Technology)

Abstract


In this paper, we establish the ergodicity of the Airy line ensemble with respect to horizontal shifts. This shows that it is the only candidate for Conjecture 3.2 in Corwin & Hammond, Invent. Math. 2014, regarding the classification of ergodic line ensembles satisfying a certain Brownian Gibbs property after a parabolic shift.


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Pages: 1-11

Publication Date: July 26, 2014

DOI: 10.1214/ECP.v19-3504

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