Convergence of the KPZ line ensemble

Abstract

In this paper we study the KPZ line ensembles under the KPZ scaling. Based on their Gibbs property, we derive quantitative local fluctuation estimates for the scaled KPZ line ensembles. This allows us to show that the family of scaled KPZ line ensembles is tight. Together with the recent progress in [QS20], [Vir], and [DM], the tightness result yields the conjectural convergence of the scaled KPZ line ensembles to the Airy line ensemble.