Ergodicity of the Airy line ensemble
Ivan Corwin, Xin Sun
TL;DR
This paper proves the ergodicity of the Airy line ensemble, confirming its unique status among line ensembles with a specific Brownian Gibbs property after a parabolic shift.
Contribution
It establishes the ergodicity of the Airy line ensemble, addressing a key conjecture in the classification of ergodic line ensembles with Brownian Gibbs property.
Findings
Proves ergodicity of the Airy line ensemble
Confirms its uniqueness among line ensembles with certain properties
Addresses a specific conjecture in the field
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.
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Taxonomy
TopicsRandom Matrices and Applications · Advanced Combinatorial Mathematics · Advanced Algebra and Geometry