Convergence of the KPZ Line Ensemble

Abstract

Abstract In this paper we study the Kardar–Parisi–Zhang (KPZ) line ensemble under the KPZ scaling. Based on their Gibbs property, we derive quantitative local fluctuation estimates for the scaled KPZ line ensemble. This allows us to show the tightness of the scaled KPZ line ensemble. Together with the recent progress in [33], [36], and [15], the tightness result yields the conjectural convergence of the scaled KPZ line ensemble to the Airy line ensemble.